The mapping class group action on the space of representations of surface groups and complex dynamics

• Project/Area Number: 20540076
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Nara Women's University
• Principal Investigator: YAMASHITA Yasushi Nara Women's University, 理学部, 教授 (70239987)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000); Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
• Keywords: 双曲幾何 / クライン群 / 複素力学系 / 分岐被覆 / 写像類群 / 語の問題

Research Abstract

I was succeeded in constructing a counter example to the conjecture on the end invariant of the character variety of the free group of rank two. This was a joint word with Prof. S.P.Tan and Prof.M.Sakuma. I have found a set of rays similar to the pleating rays in the diagonal slice of the character variety with Prof.C.Series and Prof.S.P.Tan. With Prof.Y.Rieck, I showed that the complexity of the word problem for the automorphism groups of right-angled Artin groups is bounded from above by a polynomial.

Research Products

• [Journal Article] The link volume (2011)
  • Author(s): Y.Rieck, Y.Yamashita
  • Journal Title: 結び目の数学III報告集 Pages: 185-192
• [Journal Article] Finite planar emulators for K4, 5-4K2 and K1, 2, 2, 2 and Fellows' Conjecture (2010)
  • Author(s): Y.Rieck, Y.Yamashita
  • Journal Title: European Journal of Combinatorics 31 Pages: 903-907
  • Peer Reviewed
• [Journal Article] The link volume (2010)
  • Author(s): Y.Rieck, Y.Yamashita
  • Journal Title: 研究集会「結び目の数学III」報告集 Pages: 185-191
• [Journal Article] Finite planar emulators for K_{4,5}-4K_2 and K_{1,2,2,2} and Fellows' Conjecture (2010)
  • Author(s): Y.Rieck, Y.Yamashita
  • Journal Title: European Journal of Combinatorics 31
  • Peer Reviewed
• [Journal Article] The word problems for the automorphism and outer automorphism groups of right angled Artin groups are solvable in polynomial time (2008)
  • Author(s): Y.Rieck, Y.Yamashita
  • Journal Title: Proceedings of Intelligence of low dimensional topology 2008 and the extended KOOK Seminar Pages: 111-120
• [Journal Article] OHT-A software for the dynamics of the modular group action on the character variety (2008)
  • Author(s): Y.Yamashita
  • Journal Title: 複素力学系とその周辺分野の研究,数理解析研究所講究録 1586 Pages: 18-25
• [Journal Article] The word problems for the automorphism and outer automorphism groups of right angled Artin groups are solvable in polynomial time (2008)
  • Author(s): Yoav Rieck, Yasushi Yamashita
  • Journal Title: Proceedings of Intelligence of low dimensional topology 2008 and the extended KOOK Seminar Pages: 111-120
• [Presentation] A computer experiment on primitive stable representations (2011)
  • Author(s): 山下靖
  • Organizer: National University of Singapore.
  • Year and Date: 2011-03-08
• [Presentation] The link volume of 3-manifolds (2010)
  • Author(s): Y.Rieck, Y.Yamashita
  • Organizer: 結び目の数学III
  • Place of Presentation: 日本大学
  • Year and Date: 2010-12-22
• [Presentation] A computer experiment on primitive stable representations (2010)
  • Author(s): 山下靖
  • Organizer: Hyperbolic Geometry and related topics, Koria Institute for Advanced Study
  • Place of Presentation: Korea
  • Year and Date: 2010-09-15
• [Presentation] A computer experiment on primitive stable representations (2010)
  • Author(s): 山下靖
  • Organizer: トポロジーとコンピュータ
  • Place of Presentation: 東京工業大学
  • Year and Date: 2010-09-15
• [Presentation] Computer experiments on once punctured torus groups (2010)
  • Author(s): Yasushi Yamashita
  • Organizer: Geom., Top., and Dynamics of C.V.
  • Place of Presentation: Singapore
  • Year and Date: 2010-06-30
• [Presentation] Computer experiments on once punctured torus groups (2010)
  • Author(s): 山下靖
  • Organizer: Geometry, Topology and Dynamics of Character Varieties, National University of Singapore
  • Place of Presentation: Singapore
• [Presentation] Data compression and the outer automorphism of rightangled Artin groups (2009)
  • Author(s): 山下靖
  • Organizer: Workshop on Category Theory, Computer Science and Topology
  • Place of Presentation: 信州大学
  • Year and Date: 2009-10-17
• [Presentation] Finite planar emulators and Fellows'conjecture (2009)
  • Author(s): Y.Rieck, Y.Yamashita
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-25
• [Presentation] Finite planar emulators and Fellows' conjecture (2009)
  • Author(s): 山下靖
  • Organizer: トポロジーとコンピュータ
  • Place of Presentation: 東京工業大学
  • Year and Date: 2009-09-01
• [Presentation] On Fellows'conjecture (2009)
  • Author(s): Y.Rieck, Y.Yamashita
  • Organizer: トポロジーとコンピュータ
  • Place of Presentation: 東京工業大学
  • Year and Date: 2009-08-31
• [Presentation] The word problem for the outer automorphism group of right-angled Artin groups (2009)
  • Author(s): Y.Rieck, Y.Yamashita
  • Organizer: 「リーマン面・不連続群論」研究集会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-01-12
• [Presentation] 2元生成メビウス変換群に関するJorgensenとBowditchの理論について (2008)
  • Author(s): 山下靖
  • Organizer: 第四回明治大学生田幾何セミナー
  • Place of Presentation: 明治大学
  • Year and Date: 2008-12-22
• [Presentation] Computer experiments on the growth function of twobridge link groups (2008)
  • Author(s): 山下靖
  • Organizer: Geometry & Topology seminar
  • Place of Presentation: University of Warwick, UK
  • Year and Date: 2008-11-06
• [Presentation] Computer experiraents on the growth function of two-brid ge link groups (2008)
  • Author(s): Yasushi Yamashita
  • Organizer: Geometry&Topology seminar
  • Place of Presentation: Univ. of Warwick (UK)
  • Year and Date: 2008-11-06
• [Presentation] The word problem for the automorphism and outer automorphism groups of a right-angled Artin group is solvable in polynomial time (2008)
  • Author(s): Y.Rieck, Y.Yamashita
  • Organizer: 研究集会「Intelligence of Low Dimensional Topology」兼「拡大KOOKセミナー」
  • Place of Presentation: 大阪市立大学
  • Year and Date: 2008-10-07
• [Remarks] ホームページ
  • URL: http://vivaldi.ics.nara-wu.ac.jp/~yamasita/
• [Remarks]
  • URL: http://vivaldi.ics.nara-wu.ac.jp/~yamasita/
• [Remarks]
  • URL: http://vivaldi.ics.nara-wu.ac.jp/~yamasita/
• [Remarks]
  • URL: http://vivadli.ics.nara-wu.ac.jp/~yamasita/