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2011 Fiscal Year Final Research Report

Studies of Knot Theory

Research Project

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Project/Area Number 21244005
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionOsaka City University

Principal Investigator

KAWAUCHI Akio  大阪市立大学, 大学院・理学研究科, 教授 (00112524)

Co-Investigator(Kenkyū-buntansha) KANENOBU Taizo  大阪市立大学, 大学院・理学研究科, 教授 (00152819)
TANAKA Tanaka  岐阜大学, 教育学部, 准教授 (60396851)
IWAKIRI Masahide  佐賀大学, 大学院・工学系研究科, 講師 (10453127)
MORIUCHI Hiromasa  大阪市立大学, 大学院・理学研究科, 特任助教 (20453128)
YAMAMOTO Ryousuke  群馬大学, 教育学部, 准教授 (80445006)
TAYAMA Ikuo  大阪市立大学, 大学院・理学研究科, 研究所員 (00382036)
Co-Investigator(Renkei-kenkyūsha) SAKUMA Makoto  広島大学, 大学院・理学研究科, 教授 (30178602)
NAKANISHI Yasutaka  神戸大学, 大学院・理学研究科, 教授 (70183514)
KAMADA Seiichi  広島大学, 大学院・理学研究科, 教授 (60254380)
TERAGAITO Masakazu  広島大学, 大学院・教育学研究科, 教授 (80236984)
TANIYAMA Kouki  教育・総合科学学術院, 教授 (10247207)
MOTEGI Kimihiko  日本大学, 文理学部, 教授 (40219978)
OOYAMA Toshiyuki  東京女子大学, 文理学部, 教授 (80223981)
GOUDA Hiroshi  東京農工大学, 共生科学技術研究院, 教授 (60266913)
HASHIMOTO Yoshitake  東京都市大学, 知識工学部, 教授 (20271182)
MASUDA Mikiya  大阪市立大学, 大学院・理学研究科, 教授 (00143371)
SHIMOKAWA Koya  埼玉大学, 理工学研究科, 准教授 (60312633)
SATOU Shin  神戸大学, 大学院・理学研究科, 准教授 (90345009)
Project Period (FY) 2009 – 2011
Keywords結び目理論 / 3次元多様体 / トポロジー / 空間グラフ / 数理モデル
Research Abstract

Knot theory is related to most advanced modern mathematics and also to many research fields in science. The purpose of this program was to develop、in a national scale、both education and study of an extensive knot theory on the basis of the accomplishments of the 21 COE program of Osaka City Advanced Mathematical institute. The support project of international and domestic meetings was carried out steadily、and many new findings on knot theory could be obtained. Among such research activities、unique studies of knot theory such as the publication of an English book of teaching and learning methods of knot theory in school mathematics and three patent applications of knot theory were born.

  • Research Products

    (44 results)

All 2012 2011 2010 Other

All Journal Article (24 results) (of which Peer Reviewed: 24 results) Presentation (12 results) Book (3 results) Remarks (2 results) Patent(Industrial Property Rights) (3 results)

  • [Journal Article] A Table of Genus Two Handlebody-Knots Up to Six Crossings2012

    • Author(s)
      A. Ishii, K. Kishimoto, H. Moriuchi and M. Suzuki
    • Journal Title

      Journal of Knot Theory and Its Ramifications

      Volume: Vol.21, No.4(掲載確定)

    • URL

      http://math.tsukuba.ac.jp/~aishii/files/paper020.pdf

    • Peer Reviewed
  • [Journal Article] On the Alexander polynomials of knots with Gordian distance one2012

    • Author(s)
      Akio Kawauchi
    • Journal Title

      Topology and its Applications

      Volume: Vol.159 Pages: 948-958

    • DOI

      DOI:10.1016/j.topol.2011.11.017

    • Peer Reviewed
  • [Journal Article] Finite type invariants of order 3 for a spatial handcuff graph2012

    • Author(s)
      Taizo Kanenobu and Kaori Sugita
    • Journal Title

      Topology Appl

      Volume: Vol.159 Pages: 966-979

    • DOI

      DOI:10.1016/j.topol.2011.11.016

    • Peer Reviewed
  • [Journal Article] Epimorphisms between 2-bridge links : Homotopically trivial simple loops on 2-bridge spheres2012

    • Author(s)
      Donghi Lee, Makoto Sakuma
    • Journal Title

      Proc. London Math. Soc.

      Volume: Vol.104 Pages: 359-386

    • DOI

      DOI:10.1112/plms/pdr036

    • Peer Reviewed
  • [Journal Article] Differences of Alexander polynomials for knots caused by a single crossing change2012

    • Author(s)
      Yasutaka NAKANISHI and Yuki OKADA
    • Journal Title

      Topology and its Applications

      Volume: Vol.159 Pages: 1016-1025

    • DOI

      DOI:10.1016/j.topol.2011.11.023

    • Peer Reviewed
  • [Journal Article] On the crossing numbers of a virtual knot2012

    • Author(s)
      S. Satoh and Y. Tomiyama
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: Vol.140 Pages: 367-376

    • DOI

      DOI:10.1090/S0002-9939-2011-10917-1

    • Peer Reviewed
  • [Journal Article] On transforming a spatial graph into a plane graph2011

    • Author(s)
      Akio Kawauchi
    • Journal Title

      Progress of Theoretical Physics Supplement

      Volume: Vol.191 Pages: 235-244

    • DOI

      DOI:10.1143/PTPS.191.225

    • Peer Reviewed
  • [Journal Article] Amphicheirality of links and Alexander invariants2011

    • Author(s)
      Teruhisa Kadokami and Akio Kawauchi
    • Journal Title

      SCIENCE CHINA Mathematics

      Volume: Vol.54 Pages: 2213-2227

    • DOI

      DOI:10.1007/s11425-011-4217-6

    • Peer Reviewed
  • [Journal Article] H(2)-Gordian distance of knots2011

    • Author(s)
      Taizo Kanenobu
    • Journal Title

      Journal of Knot Theory and Its Ramifications

      Volume: Vol.20 Pages: 813-835

    • DOI

      DOI:10.1142/S0218216511008991

    • Peer Reviewed
  • [Journal Article] Bridge presentations of virtual knots2011

    • Author(s)
      Mikami Hirasawa, Naoko Kamada and Seiichi Kamada
    • Journal Title

      J. Knot Theory Ramifications

      Volume: Vol.20 Pages: 881-893

    • DOI

      DOI:10.1142/S021821651100901

    • Peer Reviewed
  • [Journal Article] Infinite sequences of mutually non-conjugate surface braids representing same surface-links2011

    • Author(s)
      Masahide Iwakiri
    • Journal Title

      Proc. of the American Mathematical Society

      Volume: Vol.139 Pages: 357-366

    • DOI

      DOI:10.1090/S0002-9939-2011-10893-1

    • Peer Reviewed
  • [Journal Article] Quandle cocycle invariants for spatial graphs and knotted handlebodies2011

    • Author(s)
      A. Ishii and M. Iwakiri
    • Journal Title

      Canadian J. Math.

      Volume: Vol.63 Pages: 102-122

    • DOI

      DOI:10.4153/CJM-2011-035-0

    • Peer Reviewed
  • [Journal Article] An infinite family of Casson handles and the Rasmussen invariant of a knot2011

    • Author(s)
      Toshifumi Tanaka
    • Journal Title

      J. Knot Theory Ramifications

      Volume: Vol.20 Pages: 1229-1236

    • DOI

      DOI:10.1142/S0218216511009297

    • Peer Reviewed
  • [Journal Article] Factorization formulas and computations of higher-order Alexander invariants for homologically fibered knots2011

    • Author(s)
      Hiroshi Goda and Takuya Sakasai
    • Journal Title

      J. Knot Theory Ramifications

      Volume: Vol.20 Pages: 1355-1380

    • DOI

      DOI:10.1142/S0218216511009303

    • Peer Reviewed
  • [Journal Article] Band surgeries between knots and links with small crossing numbers2011

    • Author(s)
      Kai Ishihara and Koya Shimokawa
    • Journal Title

      Progress of Theoretical Physics Supplement

      Volume: Vol.191 Pages: 245-255

    • DOI

      DOI:10.1143/PTPS.191.245

    • Peer Reviewed
  • [Journal Article] Cyclic surgery between toroidal surgeries2011

    • Author(s)
      寺垣内政
    • Journal Title

      Canadian Mathematical Bulletin

      Volume: Vol.54 Pages: 556-560

    • DOI

      DOI:10.4153/CMB-2010-108-6

    • Peer Reviewed
  • [Journal Article] Buchstaber invariants of skeleta of a simplex2011

    • Author(s)
      Y. Fukukawa, M. Masuda
    • Journal Title

      Osaka J. Math.

      Volume: Vol.48 Pages: 549-582

    • URL

      http://projecteuclid.org/euclid.ojm/1315318353

    • Peer Reviewed
  • [Journal Article] On intrinsically knotted or completely 3-linked graphs2011

    • Author(s)
      R. Hanaki, R. Nikkuni, K. Taniyama, and A. Yamazaki
    • Journal Title

      Pacific J. Math.

      Volume: Vol.252 Pages: 407-425

    • DOI

      DOI:10.2140/pjm.2011.252.407

    • Peer Reviewed
  • [Journal Article] Enumerating 3-manifolds with lengths up to 9 by a canonical order2010

    • Author(s)
      A. Kawauchi and I. Tayama
    • Journal Title

      Topology Appl.

      Volume: Vol.157 Pages: 261-268

    • DOI

      DOI:10.1016/j.topol.2009.04.028

    • Peer Reviewed
  • [Journal Article] Upper bound for the alternation number of a torus knot2010

    • Author(s)
      Taizo Kanenobu
    • Journal Title

      Topology Appl.

      Volume: Vol.157 Pages: 302-318

    • DOI

      DOI:10.1016/j.topol.2009.04.025

    • Peer Reviewed
  • [Journal Article] Homology groups of symmetric quandles and cocycle invariants of links and surface-links2010

    • Author(s)
      Seiichi Kamada and Kanako Oshiro
    • Journal Title

      Trans. Amer. Math. Soc.

      Volume: Vol.362 Pages: 5501-5527

    • DOI

      DOI:10.1090/S0002-9947-2010-05131-1

    • Peer Reviewed
  • [Journal Article] Almost alternating knots producing an alternating knot2010

    • Author(s)
      堀内澄子, 大山淑之
    • Journal Title

      J. Knot Theory Ramifications

      Volume: Vol.19 Pages: 503-507

    • DOI

      DOI:10.1142/S0218216510007942

    • Peer Reviewed
  • [Journal Article] On Alexander polynomials of open book decompositions of 3-manifolds2010

    • Author(s)
      Ryosuke Yamamoto
    • Journal Title

      Topology Appl.

      Volume: Vol.157 Pages: 173-178

    • DOI

      DOI:10.1016/j.topol.2009.04.035

    • Peer Reviewed
  • [Journal Article] Topology of prion proteins

    • Author(s)
      Akio kawauchi and Kayo Yoshida
    • Journal Title

      Journal of Mathematics and System Science

    • URL

      http://www.sci.osaka-cu.ac.jp/~kawauchi/TopologyofPrionProteins.pdf

    • Peer Reviewed
  • [Presentation] Prime amphicheiral knots admitting a free involution2012

    • Author(s)
      作間誠
    • Organizer
      結び目理論の展望
    • Place of Presentation
      早稲田大学
    • Year and Date
      2012-03-18
  • [Presentation] Fibered knots and Seifert surfaces2012

    • Author(s)
      Hiroshi Goda
    • Organizer
      International Week celebrating the 50th anniversary of University of Nantes University of Nantes
    • Place of Presentation
      France
    • Year and Date
      2012-03-15
  • [Presentation] Tangle analysis of unlinking by XerCD-dif-FtsK system2012

    • Author(s)
      下川航也
    • Organizer
      International conference "Discrete and Topological Models in Molecular Biology"
    • Place of Presentation
      University of South Florida
    • Year and Date
      2012-03-13
  • [Presentation] Band surgery on knots with applications to other local moves2012

    • Author(s)
      Taizo Kanenobu
    • Organizer
      アメリカ数学会春期西部会合,特別会議『線形および環状ポリマーモデルにおける結び目』ハワイ大学
    • Place of Presentation
      アメリカ合衆国
    • Year and Date
      2012-03-04
  • [Presentation] Topology of prion proteins2012

    • Author(s)
      Akio Kawauchi
    • Organizer
      AMS Special Session on Knotting in Linear and Ring Polymer Models
    • Place of Presentation
      University of Hawaii at Manoa, U. S. A
    • Year and Date
      2012-03-03
  • [Presentation] Iterated circle bundles2012

    • Author(s)
      Mikiya Masuda
    • Organizer
      アメリカ数学会特別会合Transformation groups in topology
    • Place of Presentation
      ハワイ大学(アメリカ)
    • Year and Date
      2012-03-03
  • [Presentation] Twisted biquandles and invariants of twisted links2012

    • Author(s)
      S. Kamada
    • Organizer
      国際研究集会The Eighth East Asian School of Knots and Related Topics
    • Place of Presentation
      KAIST, Daejeon,韓国
    • Year and Date
      2012-01-10
  • [Presentation] Virtual graph presentations of ribbon surface-knots2012

    • Author(s)
      S. Satoh
    • Organizer
      The 8th East Asian School of Knots and Related Topics
    • Place of Presentation
      KAIST, Daejeon, Korea
    • Year and Date
      2012-01-09
  • [Presentation] 数学「結び目理論」を応用した電子ゲーム装置2011

    • Author(s)
      河内明夫
    • Organizer
      大阪府立大学・大阪市立大学新技術説明会
    • Place of Presentation
      科学技術振興機構JSTホール(東京・市ヶ谷)
    • Year and Date
      2011-10-14
  • [Presentation] 3次元多様体の列挙についての現状報告2011

    • Author(s)
      田山育男
    • Organizer
      2011年(秋季)日本数学会トポロジー分科会
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-29
  • [Presentation] On symmetry of the Jones polynomial of ribbon knots2011

    • Author(s)
      田中利史
    • Organizer
      The 3rd KOOK. TAPU Joint Seminar on Knot Theory and Related Topics
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2011-07-26
  • [Presentation] 結び目理論を応用する(清水理佳氏との共同講演)2011

    • Author(s)
      河内明夫
    • Organizer
      大阪市立大学学術戦略会議
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2011-06-14
  • [Book] 曲面結び目理論2012

    • Author(s)
      鎌田聖一
    • Total Pages
      247
    • Publisher
      丸善出版株式会社
  • [Book] Networking Seifert surgeries on knots2012

    • Author(s)
      Arnaud Deruelle, Katura Miyazaki and Kimihiko Motegi
    • Total Pages
      130
    • Publisher
      Memoirs Amer
  • [Book] Teaching and Learning of Knot Theory in School Mathematics2011

    • Author(s)
      河内明夫・柳本朋子
    • Total Pages
      188
    • Publisher
      OCAMI Studies
  • [Remarks] (ホームページ)

    • URL

      http://math01.sci.osaka-cu.ac.jp/OCAMI/index.html

  • [Remarks] (報道)朝日新聞2011年6月17日・Asahi. com 2011年6月19日,「結び目理論を応用した領域選択ゲーム」の記事

  • [Patent(Industrial Property Rights)] スイッチングシステム2012

    • Inventor(s)
      河内明夫、清水理佳、岸本健吾
    • Industrial Property Rights Holder
      公立大学法人大阪市立大学
    • Industrial Property Number
      特許、特願2012-094282
    • Filing Date
      2012-04-17
  • [Patent(Industrial Property Rights)] ゲーム装置、及びゲームプログラム2011

    • Inventor(s)
      河内明夫、清水理佳、岸本健吾
    • Industrial Property Rights Holder
      公立大学法人大阪市立大学
    • Industrial Property Number
      特許、特願2011-095520
    • Filing Date
      2011-04-21
  • [Patent(Industrial Property Rights)] ゲーム装置、及びゲームプログラム2011

    • Inventor(s)
      河内明夫、清水理佳、岸本健吾
    • Industrial Property Rights Holder
      公立大学法人大阪市立大学
    • Industrial Property Number
      特許、特願2011-158263
    • Filing Date
      2011-07-19

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Published: 2013-07-31   Modified: 2018-05-02  

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