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Innovative research of geometric topology and singularities of differentiable mappings

Research Project

Project/Area Number 17H06128
Research Category

Grant-in-Aid for Scientific Research (S)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionKyushu University

Principal Investigator

佐伯 修  九州大学, マス・フォア・インダストリ研究所, 教授 (30201510)

Co-Investigator(Kenkyū-buntansha) 大本 亨  北海道大学, 理学研究院, 教授 (20264400)
鎌田 聖一  大阪大学, 理学研究科, 教授 (60254380)
石川 昌治  慶應義塾大学, 経済学部(日吉), 教授 (10361784)
遠藤 久顕  東京工業大学, 理学院, 教授 (20323777)
岩瀬 則夫  九州大学, 数理学研究院, 教授 (60213287)
小林 真人  秋田大学, 理工学研究科, 准教授 (10261645)
Project Period (FY) 2017-05-31 – 2022-03-31
Project Status Granted (Fiscal Year 2020)
Budget Amount *help
¥81,640,000 (Direct Cost: ¥62,800,000、Indirect Cost: ¥18,840,000)
Fiscal Year 2020: ¥14,560,000 (Direct Cost: ¥11,200,000、Indirect Cost: ¥3,360,000)
Fiscal Year 2019: ¥15,470,000 (Direct Cost: ¥11,900,000、Indirect Cost: ¥3,570,000)
Fiscal Year 2018: ¥18,460,000 (Direct Cost: ¥14,200,000、Indirect Cost: ¥4,260,000)
Fiscal Year 2017: ¥18,070,000 (Direct Cost: ¥13,900,000、Indirect Cost: ¥4,170,000)
Keywords微分位相幾何 / 特異点 / 幾何的トポロジー / 低次元トポロジー / 産業数学 / 特異点論 / 特異Lefschetz束 / trisection / shadow / 安定写像 / Vassiliev型不変量 / はめ込まれた曲面結び目 / 位相的複雑さ / 特異ファイバー / 特異Lefschetz構造 / データ可視化 / 多目的最適化 / 多様体対 / 不変量
Outline of Annual Research Achievements

本研究では,トポロジーにおける幾何的アイデアを特異点論の世界に持ち込み,既存の概念・定式化・手法を革新し,写像の特異点論の飛躍的発展を図ること,そして逆に幾何的トポロジーに特異点論から新しい道を切り開き,重要な問題の解決を図ることが目的である.
平成30年度は,4次元多様体上の特異写像の変形操作のうち常に実現可能であるものをリストアップし,それを用いて写像を単純化するアルゴリズムを確立した.その結果,特異シンプレクティック構造に付随した特異Lefschetz構造の存在や,単純化されたtrisectionの存在を,具体的かつ構成的に証明することに成功した.さらに,A'Campo の divide を Turaev の shadow と関連付け,LF-property と呼ばれるLefschetz束構造を shadow の上に確立した.Shadow は3次元多様体から平面への安定写像と深く関係し,今回の研究で複素特異点とそうした安定写像を shadow という枠組みで包括的に研究する基礎付けができたことになる. 我々はさらに,3次元多様体上の安定写像に対する新しいVassiliev型不変量を構成することにも成功した.また,4次元空間にはめ込まれた曲面についても研究し,H自明と呼ばれる絡み目を新たに定式化することで,はめ込まれた曲面結び目の marked graph diagramを定式化することに成功した.ホモトピー論の側面からは,LS理論に対する手法をファイバーワイズ理論によって拡張することで位相的複雑さに応用し,向き付け不可能曲面の位相的複雑さの決定を著しく単純化することなどに成功した.その他,諸科学分野への応用についても研究し,結晶のらせん転位の数学的記述とエネルギーの計算について結果を得た.また,学術研究員を2名雇用し,幾何的トポロジーと特異点論の研究を推進した.

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

4次元多様体上の特異写像の単純化アルゴリズムを確立し,特異Lefschetz束構造から単純なtrisectionを構成する手法を開発したことは,当該分野に大きなインパクトを与えた.このことは,論文がProc. Natl. Acad. Sci. USAに掲載されたことや,国際会議における招待講演を複数依頼されたことなどからも伺える.また,複素特異点に対してA'Campoが定式化したdivideを,Turaevが量子不変量の観点から導入したshadowと関連付け,LF-propertyと呼ばれるLefschetz束構造を確立した結果は,2つの概念を意外な形で結びつけるものとして注目に値する.特にshadowは3次元多様体上の安定写像と関係し,今回の成果は複素特異点と安定写像を包括的に研究する基礎付けを与える.我々はさらに3次元多様体上の安定写像に対する新しいVassiliev型不変量を,4次元多様体の符号数を用いて構成した.こうした一連の研究は低次元幾何的トポロジーのアイデアを特異点論の世界に持ち込み,特異点論を新たに進展させるものであり,本研究課題が順調に進展していることを示す.今年度はさらに,4次元空間にはめ込まれた曲面結び目のmarked graph diagramの定式化にも成功し,研究の基礎付けも与えた.特異点を持つ結び目の困難性をH自明絡み目を定式化することで乗り越え,成果を得た.ホモトピー論的側面からは,特異点論と関係の深いLS理論の手法をファイバーワイズ理論で拡張することで位相的複雑さに応用し,今後の研究の方向性を示した.雇用した学術研究員は,特異点論に基づく同境群と古典的な多様体のSKK群の同型性を示すなど,顕著な活躍を行った.また,代表者を中心に特異点論の諸科学分野への応用共同研究を行うこともできた.総じて,本研究課題は順調に進展しているといえる.

Strategy for Future Research Activity

今後も,可微分写像の大域的特異点論の重要課題に対して,幾何的トポロジーや低次元トポロジーの手法やアイデアを本質的に用いながら,当初計画したような形で研究を進めてゆく.また,それだけではなく,多項式写像の位相的研究も進め,実代数幾何的特異点論や4次元多様体論などを駆使しながら,4次元ポアンカレ予想の否定的解決に至る可能性のある可縮4次元多様体をMilnorファイバーにもつ多項式写像芽を構成してゆく.さらに,3次元多様体上の安定写像に対して,4次元多様体の符号数を用いて構成した不変量はorder 1のVassiliev型不変量となるが,そうしたものが他にもないか,対応するVassiliev複体を計算することで詳しく調べていく.また,そうした不変量が既存の量子不変量とどう関係するのかを,4次元多様体上の安定写像とその特異ファイバーを見極めることで明らかにしてゆく.一方,3次元多様体上の安定写像の特異点集合と正則ファイバーはそれぞれ(互いに交わらない)絡み目をなすが,それらの位置関係に関する研究はこれまでになかった.そこでそれらの関係を明らかにし,特異点集合が正則ファイバーと絡まない条件を決定することで,特異点を持たない写像,すなわち沈めこみに対する応用を考える.さらに,特異点論のデータ可視化への応用として,特異ファイバーを同定するアルゴリズムを,その分類理論に基づいて確立し,具体的なデータの可視化に役立てるべく,当該分野の研究者との共同研究を推進してゆく.そのためには,位相的データ解析の手法や統計手法と組み合わせることも必要となることが予想され,そうした分野の研究者の協力を得て,研究を進めてゆく.また,写像の特異点論の立場から多目的最適化におけるパレート集合の分類や特徴づけの問題にも取り組む.

Report

(4 results)
  • 2018 Annual Research Report
  • 2017 Abstract ( PDF )   Comments on the Screening Results ( PDF )   Annual Research Report

Research Products

(107 results)

All 2019 2018 2017 Other

All Int'l Joint Research Journal Article Presentation Book Remarks Funded Workshop

  • [Int'l Joint Research] マサチューセッツ大学(米国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] VAST/ダラット大学(ベトナム)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] サンパウロ大学/Universidade Federal da Paraiba(ブラジル)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] ナント大学/Universite Nice Sophia Antipolis(フランス)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Aberdeen 大学/University of Leeds(イギリス)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] University of Massachusetts(アメリカ合衆国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Polish Academy of Sciences/Warsaw University of Technology(ポーランド)

    • Related Report
      2017 Annual Research Report
  • [Journal Article] Elimination of definite fold II2019

    • Author(s)
      O. Saeki
    • Journal Title

      Kyushu J. Math.

      Volume: 未定

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A signature invariant for stable maps of 3-manifolds into surfaces2019

    • Author(s)
      O. Saeki
    • Journal Title

      Proceedings of the Australian-Japanese Workshop on Real and Complex Singularities

      Volume: -

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Mayer-Vietoris sequence for differentiable/diffeological spaces2019

    • Author(s)
      N. Iwase, N. Izumida
    • Journal Title

      Algebraic Topology and Related Topics (Mohali, 2017), Trends in Mathematics, Birkhauser

      Volume: - Pages: 123-151

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A short proof for tc(K)=42019

    • Author(s)
      N. Iwase, M. Sakai, N. Tsutaya
    • Journal Title

      Topology Appl.

      Volume: 未定

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bifurcation sets of real polynomial functions of two variables and Newton polygons2019

    • Author(s)
      Masaharu Ishikawa, Tat-Thang Nguyen, Tien-Son Pham
    • Journal Title

      Journal of Mathematical Society of Japan

      Volume: 未定

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Milnor fibration, A'Campo's divide and Turaev's shadow2019

    • Author(s)
      Masaharu Ishikawa, Hironobu Naoe
    • Journal Title

      Proceedings of FJV2017 Kagoshima: "Singularities --- Kagoshima"

      Volume: -

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Simplified broken Lefschetz fibrations and trisections of 4-manifolds2018

    • Author(s)
      Baykur R. ?nan?、Saeki Osamu
    • Journal Title

      Proc. Natl. Acad. Sci. USA

      Volume: 115 Pages: 10894-10900

    • DOI

      10.1073/pnas.1717175115

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] An algebraic description of screw dislocations in SC and BCC crystal lattices2018

    • Author(s)
      Hamada Hiroyasu、Matsutani Shigeki、Nakagawa Junichi、Saeki Osamu、Uesaka Masaaki
    • Journal Title

      Pacific Journal of Mathematics for Industry

      Volume: 10

    • DOI

      10.1186/s40736-018-0037-8

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Presentation of immersed surface-links by marked graph diagrams2018

    • Author(s)
      Kamada Seiichi、Kawauchi Akio、Kim Jieon、Lee Sang Youl
    • Journal Title

      Journal of Knot Theory and Its Ramifications

      Volume: 27 Pages: 1850052-1850052

    • DOI

      10.1142/s0218216518500529

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Biquandle cohomology and state-sum invariants of links and surface-links2018

    • Author(s)
      Kamada Seiichi、Kawauchi Akio、Kim Jieon、Lee Sang Youl
    • Journal Title

      Journal of Knot Theory and Its Ramifications

      Volume: 27 Pages: 1843016-1843016

    • DOI

      10.1142/s0218216518430162

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Biquandle (co)homology and handlebody-links2018

    • Author(s)
      Atsushi Ishii, Masahide Iwakiri, Seiichi Kamada, Jieon Kim, Shosaku Matsuzaki, Kanako Oshiro
    • Journal Title

      Journal of Knot Theory and Its Ramifications

      Volume: 27 Pages: 1843011-1843011

    • DOI

      10.1142/s0218216518430113

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] On Gauss codes of virtual doodles2018

    • Author(s)
      Bartholomew Andrew、Fenn Roger、Kamada Naoko、Kamada Seiichi
    • Journal Title

      Journal of Knot Theory and Its Ramifications

      Volume: 27 Pages: 1843013-1843013

    • DOI

      10.1142/s0218216518430137

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Doodles on surfaces2018

    • Author(s)
      Bartholomew Andrew、Fenn Roger、Kamada Naoko、Kamada Seiichi
    • Journal Title

      Journal of Knot Theory and Its Ramifications

      Volume: 27 Pages: 1850071-1850071

    • DOI

      10.1142/s0218216518500712

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Simplified broken Lefschetz fibrations and trisections of 4-manifolds2018

    • Author(s)
      R.I. Baykur and O. Saeki
    • Journal Title

      Proc. Natl. Acad. Sci. USA

      Volume: 印刷中

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Singular fibers of stable maps of manifold pairs and their applications2018

    • Author(s)
      Oka, M*
    • Journal Title

      "Singularities and Foliations. Geometry, Topology and Applications", Araujo dos Santos, et al (Eds.), Springer Proceedings in Mathematics & Statistics

      Volume: 222 Pages: 259-294

    • DOI

      10.1007/978-3-319-73639-6

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Binary differential equation at parabolic and umbilical points for 2-parameter families of surfaces2018

    • Author(s)
      Deolindo-Silva J.L.、Kabata Y.、Ohmoto T.
    • Journal Title

      Topology and its Applications

      Volume: 234 Pages: 457-473

    • DOI

      10.1016/j.topol.2017.11.014

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A multiple conjugation biquandle and handlebody-links2018

    • Author(s)
      Atsushi Ishii, Masahide Iwakiri, Seiichi Kamada, Jieon Kim, Shosaku Matsuzaki and Kanako Oshiro
    • Journal Title

      Hiroshima Mathematical Journal

      Volume: 48 Pages: 89-117

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Theory of singular fibers and Reeb spaces for visualization2017

    • Author(s)
      O. Saeki
    • Journal Title

      “Topological Methods in Data Analysis and Visualization IV - Theory, Algorithms, and Applications”, H. Carr, C. Garth, T.Weinkauf (Eds.), Proc. Topology-Based Methods in Visualization 2015

      Volume: 報告集 Pages: 3-33

    • DOI

      10.1007/978-3-319-44684-4

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Vassiliev type invariant of order one for stable maps of 3-manifolds into surfaces2017

    • Author(s)
      佐伯修
    • Journal Title

      可微分写像の特異点論とその応用,数理解析研究所講究録

      Volume: 2049 Pages: 155-172

    • Related Report
      2017 Annual Research Report
    • Open Access
  • [Journal Article] C^1-triangulations of semialgebraic sets2017

    • Author(s)
      T. Ohmoto and M. Shiota
    • Journal Title

      Journal of Topology

      Volume: 10 Pages: 765-775

    • DOI

      10.1112/topo.12024

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Thom polynomials in A-classification I: counting singular projections of a surface2017

    • Author(s)
      T. Sasajima and T. Ohmoto
    • Journal Title

      Eroupean Math. Soc. Series of Congress Reports, IMPANGA Lecture Notes `Vector bundles, Schubert varieties, and equivariant cohomology', Birkhauser

      Volume: - Pages: 203-226

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Classical formulae on projective characters of surfaces and 3-folds, revisited2017

    • Author(s)
      T. Sasajima and T. Ohmoto
    • Journal Title

      Saitama J. Math.

      Volume: 31 Pages: 141-160

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] On the Morse-Novikov number for 2-knots2017

    • Author(s)
      Hisaaki Endo and Andrei Pajitnov
    • Journal Title

      Osaka J. Math.

      Volume: 54 Pages: 723-734

    • NAID

      120006378347

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Circle-valued Morse theory for frame spun knots and surface links2017

    • Author(s)
      Endo Hisaaki and Andrei Pajitnov
    • Journal Title

      Michigan Math. J.

      Volume: 66 Pages: 813-830

    • DOI

      10.1307/mmj/1508810816

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Chart descriptions of regular braided surfaces2017

    • Author(s)
      Kamada Seiichi、Matumoto Takao
    • Journal Title

      Topology and its Applications

      Volume: 230 Pages: 218-232

    • DOI

      10.1016/j.topol.2017.08.034

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ribbon-clasp surface-links and normal forms of immersed surface-links2017

    • Author(s)
      Kamada Seiichi、Kawamura Kengo
    • Journal Title

      Topology and its Applications

      Volume: 230 Pages: 181-193

    • DOI

      10.1016/j.topol.2017.08.033

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Gauss diagrams, unknotting numbers and trivializing numbers of spatial graphs2017

    • Author(s)
      Kaur K.、Kamada S.、Kawauchi A.、Prabhakar M.
    • Journal Title

      Topology and its Applications

      Volume: 230 Pages: 586-598

    • DOI

      10.1016/j.topol.2017.08.037

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Polynomial of an oriented surface-link diagram via quantum A_2 invariant2017

    • Author(s)
      Joung Yewon、Kamada Seiichi、Kawauchi Akio、Lee Sang Youl
    • Journal Title

      Topology and its Applications

      Volume: 231 Pages: 159-185

    • DOI

      10.1016/j.topol.2017.08.030

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] Unlinking singular locus from regular fibers and its application to submersions2019

    • Author(s)
      佐伯修
    • Organizer
      接触構造、特異点、微分方程式及びその周辺
    • Related Report
      2018 Annual Research Report
  • [Presentation] Unlinking singular locus from regular fibers and its application to submersions2019

    • Author(s)
      O. Saeki
    • Organizer
      The 14th Kagoshima Algebra-Analysis-Geometry Seminar
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Examples from our Study Group Activities in Industrial Mathematics2019

    • Author(s)
      O. Saeki
    • Organizer
      Ajou大学数学コロキウム
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Upper bound for monoidal topological complexity2019

    • Author(s)
      岩瀬則夫
    • Organizer
      福岡ホモトピー論セミナー
    • Related Report
      2018 Annual Research Report
  • [Presentation] Shadow presentation of Milnor fibers2019

    • Author(s)
      石川昌治
    • Organizer
      Workshop on Topology of Singularities
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Positive flow-spines and contact 3-manifolds2019

    • Author(s)
      石川昌治
    • Organizer
      Branched Coverings, Degenerations, and Related Topics 2019
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Abalone, Seifert fibration and coil surgery2019

    • Author(s)
      石川昌治
    • Organizer
      Geometric Topology of low dimensions
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Lifting of surface foldings in dimension 3 to braided surfaces2019

    • Author(s)
      Seiichi Kamada
    • Organizer
      The 14th East Asian Conference on Geometric Topology
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Graphic descriptions of surface foldings and braided surfaces2019

    • Author(s)
      Seiichi Kamada
    • Organizer
      2019 Winter TAPU Workshop on Knot Theory and Related Topics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Quandle colorings of knots with cut points2019

    • Author(s)
      Seiichi Kamada
    • Organizer
      AMS Spring Central and Western Joint Sectional Meeting
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Simplified broken Lefschetz fibrations and trisections of 4-manifolds2018

    • Author(s)
      O. Saeki
    • Organizer
      Intelligence of Low-dimensional Topology
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Singular locus and regular fibers, do they link each other ?2018

    • Author(s)
      O. Saeki
    • Organizer
      15th International Workshop on Real and Complex Singularities
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Simplifying broken Lefschetz fibrations and trisections of 4-manifolds2018

    • Author(s)
      O. Saeki
    • Organizer
      Four Dimensional Topology
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Elimination of definite fold for simple stable maps2018

    • Author(s)
      O. Saeki
    • Organizer
      Real Algebraic Geometry and Singularity Theory Symposium
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Examples from our Study Group Activities2018

    • Author(s)
      O. Saeki
    • Organizer
      The 2nd NIMS Industrial Math Problem Solving Workshop
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Unlinking singular locus from regular fibers and its application to submersions2018

    • Author(s)
      O. Saeki
    • Organizer
      Geometry, Topology and Dynamics Seminar (OIST)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Multiple point formulas revisited2018

    • Author(s)
      T. Ohmoto
    • Organizer
      Characteristic Classes and Singularities
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A short proof for tc(K)=42018

    • Author(s)
      Norio Iwase
    • Organizer
      International Conference on Manifolds, Groups and Homotopy
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Topological complexity from fibrewise view point2018

    • Author(s)
      Norio Iwase
    • Organizer
      Mapping Spaces in Algbraic Topology
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 3次元多様体の正フロースパインと接触構造2018

    • Author(s)
      石川昌治
    • Organizer
      微分幾何・トポロジーセミナー
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Positive flow-spines and contact 3-manifolds2018

    • Author(s)
      石川昌治
    • Organizer
      火曜トポロジーセミナー
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 3次元多様体および3次元接触多様体の複雑度について2018

    • Author(s)
      石川昌治
    • Organizer
      東京女子大学トポロジーセミナー
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] オープンブック分解のモノドロミーベクトル場のl-型フロースパインの構成2018

    • Author(s)
      石川昌治
    • Organizer
      第41回箱根セミナ(2018)
    • Related Report
      2018 Annual Research Report
  • [Presentation] 平面曲線特異点のミルナー束の shadowによる表示2018

    • Author(s)
      石川昌治
    • Organizer
      金沢大学・学習院大学合同トポロジーセミナー
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 2次元結び目のモース・ノビコフ数について2018

    • Author(s)
      遠藤久顕
    • Organizer
      トポロジー火曜セミナー(東京大学)
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Two-dimensional braids, their graphical description and application to knot theory2018

    • Author(s)
      Seiichi Kamada
    • Organizer
      The 2018 International Conference of the Honam-Youngnam Mathematical Societies
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On virtual links which are equivalent as twisted links2018

    • Author(s)
      Seiichi Kamada
    • Organizer
      The 10th KOOK-TAPU Joint Seminar on Knots and Related Topics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On surfaces immersed in 4-space2018

    • Author(s)
      Seiichi Kamada
    • Organizer
      4-Dimensional Topology
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Quandle colorings of knot diagrams with cut points2018

    • Author(s)
      Seiichi Kamada
    • Organizer
      2018琉球結び目セミナー
    • Related Report
      2018 Annual Research Report
  • [Presentation] Simplifying indefinite fibrations and trisections of 4-manifolds2018

    • Author(s)
      O. Saeki
    • Organizer
      The 13th Kagoshima Algebra-Analysis-Geometry Seminar, Kagoshima University
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Singular set and regular fibers, do they link each other?2018

    • Author(s)
      O. Saeki
    • Organizer
      特異点論とその応用【泉屋周一先生退職記念研究集会】,北海道大学
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 微分トポロジーを用いたデータの可視化2018

    • Author(s)
      佐伯修
    • Organizer
      2018年度精密工学会 春季大会シンポジウム 「AIMaP 数学応用シンポジウム:精密工学と幾何学の新たな出会い」, 中央大学 後楽園キャンパス
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Singularity at infinity of real polynomial maps of two variables2018

    • Author(s)
      石川昌治
    • Organizer
      The 13th Kagoshima Algebra-Analysis-Geometry Seminar, Kagoshima University
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Multiplication of surface-links2018

    • Author(s)
      S. Kamada
    • Organizer
      「The 13th East Asian School of Knots and Related Topics」,KAIST Daejon, Korea
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On embedded/immersed surfaces in 4-space, their braid presentations and multiplications2018

    • Author(s)
      S. Kamada
    • Organizer
      「Knotted Embeddings in Dimensions 3 and 4」, CIRM, Marseille, France
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Robot Motion Planning from Fibrewise View Point2018

    • Author(s)
      岩瀬 則夫
    • Organizer
      特異点論とその応用【泉屋周一先生退職記念研究集会】,北海道大学
    • Related Report
      2017 Annual Research Report
  • [Presentation] Topological complexity from fibrewise view point2018

    • Author(s)
      Norio Iwase
    • Organizer
      Aberdeen Topology Seminar
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Introduction to singularity theory and fiber topology in multivariate data analysis2017

    • Author(s)
      O. Saeki
    • Organizer
      Topology, Computation and Data Analysis, Dagstuhl Seminar 17292, Schloss Dagstuhl - Leibniz Center for Informatics, Germany
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Indefinite fibrations on differentiable 4-manifolds2017

    • Author(s)
      O. Saeki
    • Organizer
      Brazil-Mexico 3rd Meeting on Singularities, UNAM, Unidad Cuernavaca, Cuernavaca, Mexico
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A Vassiliev type invariant of order one for stable maps of 3-manifolds into surfaces2017

    • Author(s)
      O. Saeki
    • Organizer
      PRIMA 3rd Congress, Singularities of Spaces and Mappings, Oaxaca, Mexico
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Global aspect of singularity theory2017

    • Author(s)
      佐伯修
    • Organizer
      ベクトル値滑層分割Morse理論の構築による多数目的最適化問題の解集合の可視化,マス・フォア・インダストリ研究所短期共同研究,九州大学
    • Related Report
      2017 Annual Research Report
  • [Presentation] Simplifying indefinite fibrations on 4-manifolds2017

    • Author(s)
      O. Saeki
    • Organizer
      Geometric and Algebraic Singularity Theory, Bedlewo, Poland
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A Vassiliev type invariant of order one for stable maps of 3-manifolds into surfaces2017

    • Author(s)
      O. Saeki
    • Organizer
      Australian-Japanese Workshop on Real and Complex Singularities, The University of Sydney, Australia
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Topologia das singularidades e teoria de nos (in Portuguese)2017

    • Author(s)
      O. Saeki
    • Organizer
      IV Encontro de Singularidades no Nordeste, Departamento de Matematica da Universidade Federal da Paraiba, Joao Pessoa, Brazil
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Elimination of definite fold II2017

    • Author(s)
      O. Saeki
    • Organizer
      可微分写像の特異点論の局所的研究と大域的研究,京都大学数理解析研究所
    • Related Report
      2017 Annual Research Report
  • [Presentation] Simplifying indefinite fibrations on 4-manifolds2017

    • Author(s)
      佐伯修
    • Organizer
      半田山・代数・幾何セミナー ,岡山理科大学
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Geometric Algebra and Singularities arising in Differential Line Geometry2017

    • Author(s)
      大本亨
    • Organizer
      可微分写像の特異点論の局所的研究と大域的研究
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] C^1-triangulations and semialgebraic de Rham homotopy theory2017

    • Author(s)
      T. Ohmoto
    • Organizer
      Singularity Conference, Shanghai
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On singularities at infinity of real polynomial maps2017

    • Author(s)
      石川昌治
    • Organizer
      理科大ワークショップ,東京理科大学神楽坂キャンパス
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 4次元多様体のtrisection入門2017

    • Author(s)
      遠藤久顕
    • Organizer
      4次元多様体のtrisection勉強会
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 4次元多様体のtrisection入門2017

    • Author(s)
      遠藤久顕
    • Organizer
      N-KOOKセミナー2017年10月会合
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Introduction to trisections of 4-manifolds2017

    • Author(s)
      遠藤久顕
    • Organizer
      研究集会「4次元トポロジー」
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stabilization theorems for Lefschetz fibrations2017

    • Author(s)
      Hisaaki Endo
    • Organizer
      2017 Taiwan Mathematical Society Annual Meeting
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Doodles on surfaces2017

    • Author(s)
      S. Kamada
    • Organizer
      「Self-distributive system and quandle (co)homology theory in algebra and low-dimensional topology」, Kolon Seacloud Hotel, 釜山, 韓国
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Doodles on surfaces2017

    • Author(s)
      S. Kamada
    • Organizer
      「The 4th Russian-Chinese Conference on Knot Theory and Related Topics」, Bauman Moscow State Technical University, Moscow, Russia
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Isotopic deformations of immersed surfaces in 4-space and their braid presentations2017

    • Author(s)
      S. Kamada
    • Organizer
      「The 2nd Pan Pacific Topology Conference on Topology and Applications」, BEXCO Convention Hall, Busan, Korea
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Doodles on surfaces, virtual diagrams on the plane, and commutator identities2017

    • Author(s)
      S. Kamada
    • Organizer
      「The 7th East Asian Conference on Algebraic Topology」, IISER Mohali, Mohadi, India
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Topological complexity and fibrewise L-S category2017

    • Author(s)
      Norio Iwase
    • Organizer
      2nd Pan Pacific International Conference on Topology and Application (Algebraic Topology Session)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] クラインボトルの位相的複雑さ2017

    • Author(s)
      岩瀬 則夫
    • Organizer
      トポロジー金曜セミナー,九州大学
    • Related Report
      2017 Annual Research Report
  • [Book] 結晶の界面、転位、構造の数理2017

    • Author(s)
      松谷 茂樹,佐伯 修,中川 淳一,田上 大助,上坂 正晃,Pierluigi Cesana, 濵田 裕康
    • Total Pages
      148
    • Publisher
      九州大学マス・フォア・インダストリ研究所
    • Related Report
      2017 Annual Research Report
  • [Book] The Role and Importance of Mathematics in Innovation, Proceedings of the Forum “Math-for-Industry” 2015, Mathematics for Industry, Vol. 252017

    • Author(s)
      B. Anderssen, P. Broadbridge, Y. Fukumoto, N. Kamiyama, Y. Mizoguchi, K. Polthier, and O. Saeki
    • Total Pages
      176
    • Publisher
      Springer
    • ISBN
      9789811009624
    • Related Report
      2017 Annual Research Report
  • [Remarks] 佐伯研究室

    • URL

      http://imi.kyushu-u.ac.jp/~saeki/research-j.html

    • Related Report
      2018 Annual Research Report
  • [Remarks] 遠藤久顕 (Hisaaki Endo)

    • URL

      http://www.math.titech.ac.jp/~endo/index.html

    • Related Report
      2018 Annual Research Report
  • [Remarks] 佐伯研究室

    • URL

      http://imi.kyushu-u.ac.jp/~saeki/index-j.html

    • Related Report
      2017 Annual Research Report
  • [Funded Workshop] The 14th East Asian Conference on Geometric Topology2019

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] The 14th Kagoshima Algebra-Analysis-Geometry Seminar2019

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] The 6th Franco-Japanese-Vietnamese Symposium on Singularities2018

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] Four Dimensional Topology2018

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] The 5th Franco-Japanese-Vietnamese Symposium on Singularities, Kagoshima University2017

    • Related Report
      2017 Annual Research Report
  • [Funded Workshop] The 13th East Asian School of Knots and Related Topics, KAIST, Daejon, Korea2017

    • Related Report
      2017 Annual Research Report
  • [Funded Workshop] Geometric and Algebraic Singularity Theory, Bedlewo, Poland2017

    • Related Report
      2017 Annual Research Report
  • [Funded Workshop] Forum "Math-for-Industry" 2017, University of Hawaii at Manoa, Hawaii, United States of America2017

    • Related Report
      2017 Annual Research Report

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Published: 2017-06-01   Modified: 2020-08-26  

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