Equivariant invariants of knots and 3-manifolds

2012 Fiscal Year Final Research Report

• Project/Area Number: 21540077
• 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: OHTSUKI Tomotada 京都大学, 数理解析研究所, 教授 (50223871)
• Co-Investigator(Renkei-kenkyūsha): HABIRO Kazuo 京都大学, 数理解析研究所, 准教授 (80346064)
• Project Period (FY): 2009 – 2012
• Keywords: 結び目 / 3 次元多様体 / 不変量

Research Abstract

The author has studied invariants of knots and 3-manifolds.The author showed that the perturbative invariant is derived from the LMO invariant in the case of any simple Lie algebra in a joint work with Takahito Kuriya and Thang T. Q. Le. The author calculated the asymptoric expansion of the Kashaev invariant of some simple knots, and verified that the volume conjecture holds for these knots.

Research Products

• [Journal Article] The perturbative invariants of rational homology 3-spheres can be recovered from the LMO invariant (2012)
  • Author(s): T. Kuriya, T. T. Q. Le, T. Ohtsuki
  • Journal Title: J Topology Volume: 5 Pages: 458-484
  • DOI: doi:10.1112/jtopol/jts010
  • Peer Reviewed
• [Journal Article] Perturbative invariants of 3-manifolds with the first Betti number 1 (2010)
  • Author(s): T. Ohtsuki
  • Journal Title: Geometry and Topology Volume: 14 Pages: 1993-2045
  • DOI: DOI:10.2140/gt.2010.14.1993
  • Peer Reviewed
• [Journal Article] Invariants of knots derived from equivariant linking matricesof their surgery presentations (2009)
  • Author(s): T. Ohtsuki
  • Journal Title: Internat. J. Math Volume: 20 Pages: 883--913
  • DOI: DOI:10.1142/S0129167X09005583
  • Peer Reviewed
• [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 Pages: 527-569
  • DOI: doi:10.1112/jtopol/jtp020
  • Peer Reviewed
• [Presentation] Quantum fundamental groups of 3-manifolds I, II, III (2013)
  • Author(s): Kazuo Habiro
  • Organizer: The 9th East Asian School of Knots and Related Topics
  • Place of Presentation: Graduate School of Mathematical Sciences, University of Tokyo
  • Year and Date: 20130114-16
• [Presentation] Kirby calculus for null-homologous framed links in 3-manifolds (2013)
  • Author(s): Kazuo Habiro
  • Organizer: Low dimensional topology and number theory V
  • Place of Presentation: Soft Research Park Center, Fukuoka
  • Year and Date: 2013-03-13
• [Presentation] Quantum fundamental groups I, II, III (2012)
  • Author(s): Kazuo Habiro
  • Organizer: Winter Braids III
  • Place of Presentation: Universite de Grenoble (フランス)
  • Year and Date: 20121217-20
• [Presentation] Quantum fundamental groups of 3-manifolds, Seminaire de Topologie (2012)
  • Author(s): Kazuo Habiro
  • Organizer: Institut Mathematiques de Jussieur
  • Place of Presentation: Universite Paris 6 (フランス)
  • Year and Date: 2012-12-11
• [Presentation] Kirby calculus for null-homologous framed links in 3-manifolds (2012)
  • Author(s): Kazuo Habiro
  • Organizer: Groupe de travail TQFT et categorification
  • Place of Presentation: Institut Mathematiques de Jussieur, Universite Paris 7 (フランス)
  • Year and Date: 2012-12-10
• [Presentation] Kirby calculus for null-homologous framed links in 3-manifolds, Seminaire de Topologie (2012)
  • Author(s): Kazuo Habiro
  • Organizer: Institut Fourier
  • Place of Presentation: Universite de Grenoble (フランス)
  • Year and Date: 2012-11-23
• [Presentation] Quantum fundamental groups of 3-manifolds, Low-Dimensional Topology and Number Theory (2012)
  • Author(s): Kazuo Habiro
  • Organizer: Mathematisches
  • Place of Presentation: Forschungsinstitut Oberwolfach (ドイツ)
  • Year and Date: 2012-08-29
• [Presentation] On the structure of the mapping class category, Mapping class groups and quantum topology (2012)
  • Author(s): Kazuo Habiro
  • Organizer: IRMA
  • Place of Presentation: Strasbourg (フランス)
  • Year and Date: 2012-06-29
• [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] On the asymptotic expansion of the Kashaev invariant of knots (2012)
  • Author(s): T. Ohtsuki
  • Organizer: The 3rd GCOE Workshop for Young Mathematicians
  • Place of Presentation: Kyoto University
  • Year and Date: 2012-02-20
• [Presentation] Quantum fundamental groups of 3-manifolds, East Asian Conference on Algebraic Topology (2011)
  • Author(s): Kazuo Habiro
  • Organizer: Graduate School of Mathematical Sciences
  • Place of Presentation: University of Tokyo
  • 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 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)
  • 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: Swiss Knots 2011
  • Place of Presentation: GWATT-Zentrum, 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: 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: Institut fur Mathematik
  • Place of Presentation: Universitat Zurich (スイス)
  • 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 Mathematiques
  • Place of Presentation: Universite de Geneve (スイス)
  • Year and Date: 2010-09-16
• [Presentation] On certain limits of the reduced colored Jones polynomials of knots, Knots in Poland III (2010)
  • Author(s): Kazuo Habiro
  • Organizer: Stefan Banach International Mathematical Center
  • Place of Presentation: Bedlewo, Poland
  • Year and Date: 2010-08-02
• [Presentation] Bottom tangles and quantum link invariants, Diagram algebras and related topics (2010)
  • Author(s): Kazuo Habiro
  • Organizer: Culture Resort Festone
  • Place of Presentation: 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] (2010)
  • Author(s): 葉廣和夫
  • Organizer: 底タングルの圏と量子不変量について大談話会
  • 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 (フランス)
  • 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 (フランス)
  • 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 (フランス)
  • 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 (スイス)
  • 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 (スイス)
  • 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 Workshop "Low-dimensional topology and number theory II" (2010)
  • Author(s): Kazuo Habiro
  • Organizer: Graduate School of Mathematical Sciences
  • Place of Presentation: 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「トポロジーと写像の特異点」
  • 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, in A. Papadopoulos (ed.), Handbook of Teichmuller Theory III (2012)
  • Author(s): Kazuo Habiro and Gwenael Massuyeau
  • Total Pages: 465-530
  • Publisher: European Mathematical Society