Diffeomorphism group of the circle and discontinuous groups of theuniversal Teichmuller curve

• Project/Area Number: 22740034
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: The University of Tokyo
• Principal Investigator: MATSUDA Yoshifumi 東京大学, 大学院・数理科学研究科, 助教 (60549294)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 円周 / 微分同相群 / フックス群 / 回転数 / 収束群作用 / 相対的双曲群 / C*群環 / Cannon-Thurston写像 / 双曲群 / 普遍タイヒミュラー曲線 / C*循環 / Vietoris位相

Research Abstract

We studied a boundary of the smooth universal Teichmuller curve and the action of subgroups of diffeomorphism group of the circle on this boundary. Among actions of free product of two finite groups on the circle, we characterized Fuchsian actions in terms of rotation number.We obtained a result about simplicity of the reduced group C*-algebra of a group admitting convergence actions. We gave a necessary and sufficient condition for two geometrically finite convergence actions to admit an equivariant continuous map and applied it to construct examples of convergence actions.

Research Products

• [Journal Article] On Cannon-Thurston maps for relatively hyperbolic groups
  • Author(s): Y. Matsuda and S. Oguni
  • Journal Title: J. Group theory Volume: (掲載決定)
  • Peer Reviewed
• [Journal Article] C*-simplicity for groups with non-elementary convergence group actions
  • Author(s): Y. Matsuda, S. Oguni and S. Yamagata
  • Journal Title: Houston J. Math Volume: (掲載決定)
  • Peer Reviewed
• [Journal Article] C*-simplicity for groups with non-elementary convergence group actions
  • Author(s): Y.Matsuda, S.Oguni, S.Yamagata
  • Journal Title: Houston J.Math. Volume: (掲載確定)
  • Peer Reviewed
• [Presentation] Blowing up and down compacta with geometrically finite convergence actions of a group (2012)
  • Author(s): Y. Matsuda
  • Organizer: Rigidity School Tokyo 2011/2012
  • Place of Presentation: 東京大学
  • Year and Date: 2012-03-19
• [Presentation] Blowing up and down compacta with geometrically finite convergence actions of a group (2012)
  • Author(s): Yoshifumi Matsuda
  • Organizer: Rigidity School Tokyo 2011/2012
  • Place of Presentation: 東京大学(招待講演)
  • Year and Date: 2012-03-19
• [Presentation] The universal relatively hyperbolic structure on a group and relative quasiconvexity for subgroups (2011)
  • Author(s): Y. Matsuda
  • Organizer: Geometry and dynamics
  • Place of Presentation: リヨン高等師範学校(フランス)
  • Year and Date: 2011-10-16
• [Presentation] The universal relatively hyperbolic structure on a group and relative quasiconvexity for subgroups (2011)
  • Author(s): Yoshifumi Matsuda
  • Organizer: Geometry and dynamics
  • Place of Presentation: リヨン高等師範学校(フランス)(招待講演)
  • Year and Date: 2011-10-16
• [Presentation] On the isometry group of the universal Teichmuller curve, Workshop(s) (2010)
  • Author(s): Y. Matsuda
  • Organizer: Lefschetz fibration and category theory
  • Place of Presentation: 大阪大学
  • Year and Date: 2010-06-11
• [Presentation] On the isometry group of the universal Teichmuller curve (2010)
  • Author(s): Yoshifumi MASTSUDA
  • Organizer: Workshop(s) : Lefschetz fibration and category theory
  • Place of Presentation: 大阪大学
  • Year and Date: 2010-06-11