Algebraic study on low-dimensional topology

• Project/Area Number: 21540078
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Kyoto University
• Principal Investigator: HABIRO Kazuo 京都大学, 数理解析研究所, 准教授 (80346064)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 位相幾何学 / 3次元多様体 / 絡み目 / 量子不変量 / トポロジー / 多様体 / 埋め込み / 基本群 / 量子基本群 / 量子表現空間 / van Kampen定理 / 2重圏 / 結び目 / 底タングル / 3次元様体 / Jones多項式 / 量子化 / 表現多様体 / 分類空間 / コボルディズム / ホモロジーシリンダー / 曲面 / Kirbyカルキュラス / 色つきJones多項式

Research Abstract

We studied on several topics in 3-dimensional topology. Jointly with G. Massuyeau, we completed a survey article on homology cylinders over surfaces. We also studied Kirby calculus for framed links in 3-manifolds, power series expansions of the reduced colored Jones polynomials of knots called the"heads"and"tails", and the quantum fundamental groups and the quantum representation varieties for 3-manifolds.

Research Products

• [Journal Article] Symplectic Jacobi diagrams and the Lie algebra of homology cylinders (2009)
  • Author(s): Kazuo Habiro and Gwenael Massuyeau
  • Journal Title: J. Topology Volume: 2 Issue: 3 Pages: 527-569
  • DOI: 10.1112/jtopol/jtp020
  • Peer Reviewed
• [Journal Article] Symplectic Jacobi diagrams and the Lie algebra of homology cylinders (2009)
  • Author(s): K.Habiro, G.Massuyeau
  • Journal Title: Journal of Topology 2 Pages: 527-569
  • Peer Reviewed
• [Presentation] Quantum representation varieties as pseudo double functors (2012)
  • Author(s): Kazuo Habiro
  • Organizer: Low Dimensional Topology and Number Theory IV
  • Place of Presentation: Kyushu University, Fukuoka
  • Year and Date: 2012-03-13
• [Presentation] Quantum representation varieties as pseudo double functors (2012)
  • Author(s): Kazuo Habiro
  • Organizer: Low Dimensional Topology and Number Theory IV
  • Place of Presentation: 九州大学大学院数理学研究院(招待講演)
  • Year and Date: 2012-03-13
• [Presentation] Quantum fundamental groups of 3-manifolds (2011)
  • Author(s): Kazuo Habiro
  • Organizer: East Asian Conference on Algebraic Topology Graduate School of Mathematical Sciences
  • Place of Presentation: University of Tokyo
  • Year and Date: 2011-12-05
• [Presentation] Quantum fundamental groups of 3-manifolds (2011)
  • Author(s): Kazuo Habiro
  • Organizer: East Asian Conference on Algebraic Topology
  • Place of Presentation: 東京大学大学院数理科学研究科(招待講演)
  • Year and Date: 2011-12-05
• [Presentation] Quantum fundamental groups and quantum representation varieties of 3-manifolds (2011)
  • Author(s): 葉廣和夫
  • Organizer: トポロジー金曜セミナー
  • Place of Presentation: 九州大学数理学研究院
  • Year and Date: 2011-11-16
• [Presentation] Quantum fundamental groups and quantum representation varieties of 3-manifolds (2011)
  • Author(s): 葉廣和夫
  • Organizer: トポロジー金曜セミナー
  • Place of Presentation: 九州大学大学院数理学研究院(招待講演)
  • Year and Date: 2011-11-16
• [Presentation] Quantum fundamental groups of 3-manifolds (2011)
  • Author(s): Kazuo Habiro
  • Organizer: Geometry & Topology Down Under
  • Place of Presentation: University of Melbourne
  • Year and Date: 2011-07-21
• [Presentation] Quantum fundamental groups of 3-manifolds (2011)
  • Author(s): Kazuo Habiro
  • Organizer: Geometry & Topology Down Under
  • Place of Presentation: University of Melbourne(オーストラリア)(招待講演)
  • Year and Date: 2011-07-21
• [Presentation] Quantum fundamental groups and quantum representation varieties for 3-manifolds (2011)
  • Author(s): Kazuo Habiro
  • Organizer: Geometric and analytic approaches to representations of a group and representation spaces
  • Place of Presentation: RIMS, Kyoto University
  • Year and Date: 2011-06-20
• [Presentation] Quantum fundamental groups and quantum representation varieties for 3-manifolds (2011)
  • Author(s): Kazuo Habiro
  • Organizer: Geometric and analytic approaches to representations of a group and representation spaces
  • Place of Presentation: 京都大学数理解析研究所(招待講演)
  • Year and Date: 2011-06-20
• [Presentation] Quantum fundamental groups and quantum representation varieties for 3-manifolds (2011)
  • Author(s): Kazuo Habiro
  • Organizer: Swiss Knots 2011
  • Place of Presentation: Lake Thun, Switzerland
  • Year and Date: 2011-05-25
• [Presentation] Quantum fundamental groups and quantum representation varieties for 3-manifolds (2011)
  • Author(s): Kazuo Habiro
  • Organizer: Swiss Knots 2011
  • Place of Presentation: GWATT-zentrum,(スイス)(招待講演)
  • Year and Date: 2011-05-25
• [Presentation] Quantum fundamental groups and quantum representation varieties for 3-manifolds (2011)
  • Author(s): Kazuo Habiro
  • Organizer: Low dimensional topology and number theory III
  • Place of Presentation: Nishijin Plaza, Fukuoka
  • Year and Date: 2011-03-16
• [Presentation] Quantum fundamental groups and quantum representation varieties for 3-manifolds (2011)
  • Author(s): Kazuo Habiro
  • Organizer: Low dimensional topology and number theory III
  • Place of Presentation: 西新プラザ、福岡市(招待講演)
  • Year and Date: 2011-03-16
• [Presentation] Quantum fundamental groups and quantum representation varieties for 3-manifolds (2011)
  • Author(s): Kazuo Habiro
  • Organizer: Institut fur Mathematik
  • Place of Presentation: Universitat Zurich
  • Year and Date: 2011-02-03
• [Presentation] Quantum fundamental groups and quantum representation varieties for 3-manifolds (2010)
  • Author(s): 葉廣和夫
  • Organizer: 信州トポロジーセミナー
  • Place of Presentation: 信州大学理学部数理・自然情報科学科
  • Year and Date: 2010-12-15
• [Presentation] Quantum fundamental groups and quantum representation varieties for 3-manifolds (2010)
  • Author(s): 葉廣和夫
  • Organizer: 幾何学コロキウム
  • Place of Presentation: 北海道大学大学院理学研究院数学部門
  • Year and Date: 2010-12-09
• [Presentation] Quantum fundamental groups and quantum representation varieties for 3-manifolds (2010)
  • Author(s): 葉廣和夫
  • Organizer: トポロジー火曜セミナー
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2010-10-26
• [Presentation] Quantum fundamental groups and quantum representation varieties for 3-manifolds (2010)
  • Author(s): Kazuo Habiro
  • Organizer: Section de Mathemati ques
  • Place of Presentation: Universite de Geneve
  • Year and Date: 2010-09-16
• [Presentation] On certain limits of the reduced colored Jones polynomials of knots (2010)
  • Author(s): Kazuo Habiro
  • Organizer: Knots in Poland III
  • Place of Presentation: Stefan Banach International Mathematical Center, Bedlewo, Poland
  • Year and Date: 2010-08-02
• [Presentation] On certain limits of the reduced colored Jones polynomials of knots (2010)
  • Author(s): Kazuo Habiro
  • Organizer: Knots in Poland III
  • Place of Presentation: Stefan Banach International Mathematical Center, Bedlewo, Poland(招待講演)
  • Year and Date: 2010-08-02
• [Presentation] Bottom tangles and quantum link invariants (2010)
  • Author(s): Kazuo Habiro
  • Organizer: Diagram algebras and related topics
  • Place of Presentation: Culture Resort Festone, Ginowan, Okinawa
  • Year and Date: 2010-07-07
• [Presentation] Clasper surgeries and Brunnian links (2010)
  • Author(s): Kazuo Habiro
  • Organizer: International Conference on Algebraic and Geometric Topology
  • Place of Presentation: Capital Normal University, Beijing(中国)
  • Year and Date: 2010-07-02
• [Presentation] 底タングルの圏と量子不変量について (2010)
  • Author(s): 葉廣和夫
  • Organizer: 大談話会
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-05-26
• [Presentation] Refined Kirby calculus for closed 3-manifolds (2010)
  • Author(s): Kazuo Habiro
  • Organizer: Seminaire Quantique
  • Place of Presentation: IRMA, Strasbourg
  • Year and Date: 2010-05-03
• [Presentation] Refined Kirby calculus for closed 3-manifolds (2010)
  • Author(s): Kazuo Habiro
  • Organizer: Seminaire de Topologie
  • Place of Presentation: Institut Mathematique de Jussieu, Universite Paris 7
  • Year and Date: 2010-04-27
• [Presentation] On certain limits of the reduced colored Jones polynomials of knots (2010)
  • Author(s): Kazuo Habiro
  • Organizer: Topologie algebrique et quantique
  • Place of Presentation: CIRM, Luminy
  • Year and Date: 2010-04-22
• [Presentation] On certain limits of the reduced colored Jones polynomials (2010)
  • Author(s): Kazuo Habiro
  • Organizer: Institut fur Mathematik
  • Place of Presentation: Universitat Zurich
  • Year and Date: 2010-04-13
• [Presentation] Refined Kirby calculus for closed 3-manifolds (2010)
  • Author(s): Kazuo Habiro
  • Organizer: Institut fur Mathematik
  • Place of Presentation: Universitat Zurich
  • Year and Date: 2010-04-12
• [Presentation] 結び目のreduced colored Jones polynomialについて (2010)
  • Author(s): 葉廣和夫
  • Organizer: 新KOOKセミナー
  • Place of Presentation: 大阪市立大学文化交流センター
  • Year and Date: 2010-04-10
• [Presentation] On the reduced colored Jones polynomial of links (2010)
  • Author(s): Kazuo Habiro
  • Organizer: Low-dimensional topology and number theory II
  • Place of Presentation: Graduate School of Mathematical Sciences, University of Tokyo
  • Year and Date: 2010-03-17
• [Presentation] 底タングルと量子不変量について (2009)
  • Author(s): 葉廣和夫
  • Organizer: 大岡山談話会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2009-12-16
• [Presentation] 絡み目とホモロジー3次元球面の量子不変量 (2009)
  • Author(s): 葉廣和夫
  • Organizer: 講演会
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2009-06-13
• [Presentation] コボルディズム圏のnerveとcyclic nerveについて (2009)
  • Author(s): 葉廣和夫
  • Organizer: 研究集会
  • Place of Presentation: 信州大学理学部
  • Year and Date: 2009-06-04
• [Book] From mapping class groups to monoids of homology cobordisms : a survey, to appear in : A. Papadopoulos(Ed.) Handbook of Teichmuller Theory
  • Author(s): Kazuo Habiro and Gwenael Massuyeau
  • Publisher: European Mathematical Society
• [Remarks]
  • URL: http://www.kurims.kyoto-u.ac.jp/~habiro/
• [Remarks]
  • URL: http://www.kurims.kyoto-u.ac.jp/ja/list/habiro.html
• [Remarks]
  • URL: http://www.kurims.kyoto-u.ac.jp/~habiro