Measure-theoretic rigidity for lattices in semisimple Lie groups

• Project/Area Number: 19840005
• Research Category: Grant-in-Aid for Young Scientists (Start-up)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Tohoku University
• Principal Investigator: KIDA Yoshikata Tohoku University, 大学院・理学研究科, 助教 (90451517)
• Project Period (FY): 2007 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,105,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥405,000); Fiscal Year 2008: ¥1,755,000 (Direct Cost: ¥1,350,000、Indirect Cost: ¥405,000); Fiscal Year 2007: ¥1,350,000 (Direct Cost: ¥1,350,000)
• Keywords: 離散群 / 測度同値 / 軌道同値

Research Abstract

各単純因子の実階数が2以上の半単純リー群の格子部分群による、測度空間上の作用に関する剛性を証明した。つまり、そのような格子部分群の自己MEカップリングからそれが属するリー群への同変写像を構成した。また、曲面の写像類群による作用からできる測度論的同値関係の外部自己同型群を調べ、特に、曲面上の単純閉曲線を用いて定義される一般化されたベルヌーイ作用に対し、その群を計算した。

Research Products

• [Journal Article] The mapping class group from the viewpoint of measure equivalence theory (2008)
  • Author(s): Yoshikata Kida
  • Journal Title: Memoirs of the American Mathematical Society 196 Pages: 1-190
  • Peer Reviewed
• [Journal Article] Outer automorphism groups of equivalence relations for mapping class groups actions (2008)
  • Author(s): Yoshikata Kida
  • Journal Title: Journal of the London Mathematical Society, 2^<nd> Series, 78 Pages: 622-638
  • Peer Reviewed
• [Journal Article] Orbit equivalence rigidity for ergodic actions of mapping class groups (2008)
  • Author(s): Yoshikata Kida
  • Journal Title: Geometrie Dedicata 131 Pages: 99-109
  • Peer Reviewed
• [Journal Article] Outer automorphism groups of equivalence relations for mapping class group actions (2008)
  • Author(s): Yoshikata Kida
  • Journal Title: Journal of the London Mathematical Society 78 Pages: 622-638
  • Peer Reviewed
• [Journal Article] Orbit equivalence rigidity for ergodic actions of the mapping class group (2008)
  • Author(s): Yoshikata Kida
  • Journal Title: Geometriae Dedicata 131 Pages: 99-109
  • Peer Reviewed
• [Presentation] Orbit equivalence rigidity for mapping class groups (2008)
  • Author(s): 木田良才
  • Organizer: 第55回トポロジーシンポジウム
  • Place of Presentation: 金沢市文化ホール
  • Year and Date: 2008-08-09
• [Presentation] Orbit equivalence rigidity for some groups acting on trees (2008)
  • Author(s): Yoshikata Kida
  • Organizer: The 1^<st> MSJ-SI, Probabilistic Approach to Geomety
  • Place of Presentation: 京都大学
  • Year and Date: 2008-08-04
• [Presentation] Orbit equivalence rigidity for some groups acting on trees (2008)
  • Author(s): Yoshikata Kida
  • Organizer: The 1^<st> MSJ-SI, Probabilistic Approach to Geometry
  • Place of Presentation: 京都大学
  • Year and Date: 2008-08-04
• [Presentation] Orbit equivalence rigidity for mapping class groups (2008)
  • Author(s): Yoshikata Kida
  • Organizer: JAMI conference, Geometric Group Theory, Geometric Analysis, and Mapping Class Groups
  • Place of Presentation: Jons Hopkins 大学 (アメリカ)
  • Year and Date: 2008-05-05
• [Presentation] Orbit equivalence rigidity for mapping class groups (2008)
  • Author(s): Yoshikata Kida
  • Organizer: JAMI conference, Geometric Group Theory, Geometric Analysis, and Mapping Class Groups
  • Place of Presentation: Jons Hopkins大学 (アメリカ)
  • Year and Date: 2008-05-05
• [Presentation] Orbit equivalence and measurable group theory (2008)
  • Author(s): 木田良才
  • Organizer: 日本数学会幾何学分科会特別講演
  • Place of Presentation: 近畿大学
  • Year and Date: 2008-03-23
• [Presentation] Measurable rigidity for mapping class groups (2007)
  • Author(s): 木田良才
  • Organizer: 第54回幾何学シンポジウム
  • Place of Presentation: 鹿児島大学
  • Year and Date: 2007-08-26
• [Presentation] Measurable rigidity for mapping class groups (2007)
  • Author(s): 木田 良才
  • Organizer: 第54回幾何学シンポジウム
  • Place of Presentation: 近畿大学
  • Year and Date: 2007-08-26
• [Presentation] Orbit equivalence rigidity for ergodic actions of mapping class groups (2007)
  • Author(s): Yoshikata Kida
  • Organizer: Hyperbolic structures on 3-manifolds and large scale geometry of Teichmuller space
  • Place of Presentation: Warwick 大学 (イギリス)
  • Year and Date: 2007-07-19
• [Presentation] Orbit equivalence rigidity for ergodic actions of mapping class groups (2007)
  • Author(s): Yoshikata Kida
  • Organizer: Hyperbolic structures on 3-manifolds and large scale geometry of Teichmuller space
  • Place of Presentation: Warwick大学(イギリス)
  • Year and Date: 2007-07-19