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2014 Fiscal Year Annual Research Report

無限群と幾何学の新展開

Research Project

Project/Area Number 24224002
Research InstitutionThe University of Tokyo

Principal Investigator

坪井 俊  東京大学, 数理(科)学研究科(研究院), 教授 (40114566)

Co-Investigator(Kenkyū-buntansha) 河澄 響矢  東京大学, 数理(科)学研究科(研究院), 准教授 (30214646)
足助 太郎  東京大学, 数理(科)学研究科(研究院), 准教授 (30294515)
藤原 耕二  京都大学, 理学(系)研究科(研究院), 教授 (60229078)
大鹿 健一  大阪大学, 理学(系)研究科(研究院), 教授 (70183225)
小林 俊行  東京大学, 数理(科)学研究科(研究院), 教授 (80201490)
小島 定吉  東京工業大学, 情報理工学(系)研究科, 教授 (90117705)
Project Period (FY) 2012-05-31 – 2017-03-31
Keywords無限群 / 幾何学 / 空間形 / 多様体 / 微分同相群 / 力学系 / 写像類群 / 野性的空間
Outline of Annual Research Achievements

[空間形と無限群]について小島、大鹿、小林、金井、森吉、松田のグループで、[多様体の微分同相群]については坪井、小林、足助、松元、森田、森吉、高村のグループで、[曲面の写像類群]については、大鹿、藤原、河澄、足助、森田、皆川のグループで、[無限群の力学系的不変量]については、坪井、松元、金井、中山、林、野田、皆川、浅岡、児玉のグループで、[無限群と野生的空間]については、小島、大鹿、藤原、河澄、中山、林、浅岡のグループで共同研究を継続した。研究支援員を7名雇用し研究を推進した。
研究交流に関して、主催または共催した研究集会、国際会議の主なものは、Rigidity School, Tokyo 2014 (6月13日~6月15日)、トポロジーシンポジウム (7月26日~7月29日)、The 7th MSJ Seasonal Institute on Hyperbolic Geometry and Geometric Group Theory (7月30日~8月5日)、「葉層構造と微分同相群2014研究集会」(Foliations and Diffeomorphism Groups 2014) (10月20日~10月24日)、Rigidity School, Tokyo 2014 (2nd) (11月22日~11月24日)、「複素解析的ベクトル場・葉層構造とその周辺」 (12月12日~12月14日)である。2014年8月に、韓国ソウル市で国際数学者会議が開催され、その様々なサテライト国際会議で、研究分担者、連携研究者の成果発表が行われた。
研究分担者 藤原は、Mladen Bestvina, Kenneth Brombergと共同で、擬ツリーへの群作用の理論を確立し、諸問題に応用する論文を出版した。大鹿はクライン群の変形空間の境界を研究し論文を出版した。

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

研究代表者、研究分担者、連携研究者の研究は、特に重点をおく[空間形と無限群]、[多様体の微分同相群]、[曲面の写像類群]、[無限群の力学系的不変量]、[無限群と野生的空間]の5つについての共同研究を行って、研究交流を進めた結果、5つの研究にまたがる著しい結果が多く得られ、これらは順次、国際会議、学会で発表され、論文としても一流の数学学術雑誌に順調に出版されている。
この研究課題の研究も含めた評価により、研究分担者 小林俊行は平成26年春の紫綬褒章(数学研究功績)を受章した。また2014年度日本数学会秋季総合分科会で、研究分担者 大鹿健一が総合講演を行っている。
このように、外部からもよい評価を受けつつ、研究が順調に進展しており、予定どおりの成果が見込まれる。

Strategy for Future Research Activity

5つのグループの共同研究を全体としてまとめていく研究方法を継続すれば, 十分に研究成果が見込まれる. 無限群と幾何学の合流する点での問題ととらえることを続けていくことが重要と考える。研究分担者, 連携研究者との共同研究をさらに緊密にし、さらに広い視点を取り込んで研究を継続する。特に、空間形と無限群、多様体の微分同相群の研究を微分方程式と表現論の観点を加えて強化するために研究分担者に大島利雄を加える予定である.

  • Research Products

    (34 results)

All 2015 2014

All Journal Article (14 results) (of which Int'l Joint Research: 6 results,  Peer Reviewed: 14 results) Presentation (20 results) (of which Int'l Joint Research: 15 results,  Invited: 19 results)

  • [Journal Article] Vector-valued covariant differential operators for the Mobius transformation2015

    • Author(s)
      T. Kobayashi, T. Kubo, and M. Pevzner
    • Journal Title

      Springer Proceedings in Mathematics & Statistics

      Volume: 111 Pages: 67-86

    • DOI

      10.1007/978-4-431-55285-7_6

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Constructing group actions on quasi-trees and applications to mapping class groups2015

    • Author(s)
      Mladen Bestvina, Kenneth Bromberg, Koji Fujiwara
    • Journal Title

      Publ. IHES

      Volume: 122 Pages: 1-64

    • DOI

      10.1007/s10240-014-0067-4

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Reduced Bers boundaries of Teichmuller spaces2014

    • Author(s)
      K. Ohshika
    • Journal Title

      Ann. Inst. Fourier

      Volume: 64 Pages: 145-176

    • Peer Reviewed
  • [Journal Article] Primitive stable representations of free Kleinian groups2014

    • Author(s)
      W. Jeon, I. Kim, K. Ohshika and C. Lecuire
    • Journal Title

      Israel J. Math

      Volume: 199 Pages: 841-866

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Primitive stable closed hyperbolic 3-manifolds2014

    • Author(s)
      I. Kim, C. Lecuire and K. Ohshika
    • Journal Title

      Topology Appl.

      Volume: 172 Pages: 68-71

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Shintani functions, real spherical manifolds, and symmetry breaking operators2014

    • Author(s)
      T. Kobayashi
    • Journal Title

      Developments in Mathematics

      Volume: 37 Pages: 127-159

    • DOI

      10.1007/978-3-319-09934-7_5

    • Peer Reviewed
  • [Journal Article] Symmetric pairs with finite-multiplicity property for branching laws of admissible representations2014

    • Author(s)
      T. Kobayashi
    • Journal Title

      Proc. Japan Acad., Ser. A

      Volume: 90 Pages: 79-83

    • DOI

      10.3792/pjaa.90.79

    • Peer Reviewed
  • [Journal Article] Classification of finite-multiplicity symmetric pairs,2014

    • Author(s)
      T. Kobayashi and T. Matsuki
    • Journal Title

      Transformation Groups

      Volume: 19 Pages: 457-493

    • DOI

      10.1007/s00031-014-9265-x

    • Peer Reviewed
  • [Journal Article] Intertwining operators and the restriction of representations of rank one orthogonal groups2014

    • Author(s)
      T. Kobayashi and B. Speh
    • Journal Title

      C. R. Acad. Sci. Paris, Ser. I

      Volume: 352 Pages: 89-94

    • DOI

      10.1016/j.crma.2013.11.018

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] F-method for symmetry breaking operators2014

    • Author(s)
      T. Kobayashi
    • Journal Title

      Differential Geometry and its Applications

      Volume: 33 Pages: 272―289

    • DOI

      10.1016/j.difgeo.2013.10.003

    • Peer Reviewed
  • [Journal Article] Special functions in minimal representations2014

    • Author(s)
      T. Kobayashi
    • Journal Title

      Contemporary Mathematics

      Volume: 610 Pages: 258―266

    • DOI

      10.1090/conm/610/12103

    • Peer Reviewed
  • [Journal Article] Minimal representations via Bessel operators2014

    • Author(s)
      J. Hilgert, T. Kobayashi, and J. Moellers
    • Journal Title

      J. Math. Soc. Japan

      Volume: 66 Pages: 349-414

    • DOI

      10.2969/jmsj/06620349

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] The logarithms of Dehn twists2014

    • Author(s)
      N. Kawazumi and Y. Kuno
    • Journal Title

      Quantum Topology

      Volume: 5 Pages: 347-423

    • Peer Reviewed
  • [Journal Article] Generators of the homological Goldman Lie algebra2014

    • Author(s)
      N. Kawazumi, Y. Kuno and K. Toda
    • Journal Title

      Osaka J. Math.

      Volume: 51 Pages: 665-671

    • Peer Reviewed
  • [Presentation] Rigidity in geometry and spectral analysis on non-Riemannian locally homogeneous manifolds2015

    • Author(s)
      T. Kobayashi
    • Organizer
      Workshop: Deformation of Discrete Groups and Related Topics
    • Place of Presentation
      Nagoya University
    • Year and Date
      2015-02-17 – 2015-02-18
    • Int'l Joint Research / Invited
  • [Presentation] Group Actions and Representation Theory of Lie Groups2014

    • Author(s)
      T. Kobayashi
    • Organizer
      Visible Actions and Multiplicity-free Representations on Complex Manifolds
    • Place of Presentation
      Tohoku University
    • Year and Date
      2014-12-16 – 2014-12-19
    • Int'l Joint Research / Invited
  • [Presentation] Hyperbolic 3-manifolds and the Schottky space viewed as lying in the character variety2014

    • Author(s)
      K. Ohshika
    • Organizer
      Group Action Forum, Tsinghua-Sanya Mathematical Forum
    • Place of Presentation
      Sanya, China
    • Year and Date
      2014-12-16
    • Int'l Joint Research / Invited
  • [Presentation] Stable commutator length on mapping class groups2014

    • Author(s)
      Koji Fujiwara
    • Organizer
      Geometric and Combinatorial Group Theory In honor of Eliyahu Rips workshop
    • Place of Presentation
      Hebrew U, Israel
    • Year and Date
      2014-12-15
    • Int'l Joint Research / Invited
  • [Presentation] Symmetry Breaking Operators for Rank One Orthogonal Groups2014

    • Author(s)
      T. Kobayashi
    • Organizer
      Analysis, Geometry and Representations on Lie Groups and Homogeneous Spaces
    • Place of Presentation
      Marrakech, Morocco
    • Year and Date
      2014-12-08 – 2014-12-12
    • Int'l Joint Research / Invited
  • [Presentation] Goldman-Turaev Lie 双代数のテンソル表示について2014

    • Author(s)
      河澄響矢
    • Organizer
      多様体のトポロジーの展望
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2014-11-28
    • Invited
  • [Presentation] Symmetry Breaking Operators and Branching Problems2014

    • Author(s)
      T. Kobayashi
    • Organizer
      Symposium on Representation Theory 2014
    • Place of Presentation
      Awajishima
    • Year and Date
      2014-11-25 – 2014-11-28
    • Int'l Joint Research / Invited
  • [Presentation] Continuous deformation of geometric limits and the Maskit combination spaces2014

    • Author(s)
      K. Ohshika
    • Organizer
      Atelier de travail franco-japonais sur la geometrie des groupes modulaire et des espaces de Teichmuller
    • Place of Presentation
      Osaka Univ.
    • Year and Date
      2014-10-17
    • Int'l Joint Research / Invited
  • [Presentation] Klein 群の幾何とその応用2014

    • Author(s)
      大鹿健一
    • Organizer
      日本数学会総合講演
    • Place of Presentation
      広島大学.
    • Year and Date
      2014-09-26
    • Invited
  • [Presentation] Turaev 余括弧積, 榎本-佐藤 traces そして柏原 Vergne 問題における発散 cocycle2014

    • Author(s)
      河澄響矢
    • Organizer
      日本数学会トポロジー分科会
    • Place of Presentation
      広島大学.
    • Year and Date
      2014-09-26
  • [Presentation] The Turaev cobracket, the Enomoto-Satoh traces and the divergence cocycle in the Kashiwara-Vergne problem2014

    • Author(s)
      N. Kawazumi
    • Organizer
      Mapping class groups of surfaces and automorphism groups of free groups
    • Place of Presentation
      IRMA, University of Strasbourg
    • Year and Date
      2014-09-10
    • Int'l Joint Research / Invited
  • [Presentation] Asymptotically isometric metrics on hyperbolic groups2014

    • Author(s)
      Koji Fujiwara
    • Organizer
      The 10th Geometry conference for the friendship between China and Japan
    • Place of Presentation
      Fudan University, China
    • Year and Date
      2014-09-07 – 2014-09-11
    • Int'l Joint Research / Invited
  • [Presentation] Symmetry Breaking Operators for Rank One Orthogonal Groups2014

    • Author(s)
      T. Kobayashi
    • Organizer
      Prehomogeneous Vector Spaces and Related Topics
    • Place of Presentation
      Prehomogeneous Vector Spaces and Related Topics
    • Year and Date
      2014-09-01 – 2014-09-05
    • Invited
  • [Presentation] Quasi-homomorphisms into non-commutative groups2014

    • Author(s)
      Koji Fujiwara
    • Organizer
      Geometry on Groups and Spaces
    • Place of Presentation
      KAIST, Daejeon, Korea
    • Year and Date
      2014-08-07 – 2014-08-12
    • Int'l Joint Research / Invited
  • [Presentation] Derivatives of the Godbillon-Vey class and transverse projective structures of foliations2014

    • Author(s)
      Taro Asuke
    • Organizer
      29th Summer Conference on Topology and its Applications
    • Place of Presentation
      College of Staten Island
    • Year and Date
      2014-07-23
    • Int'l Joint Research / Invited
  • [Presentation] Branching Problems of Representations of Real Reductive Groups2014

    • Author(s)
      T. Kobayashi
    • Organizer
      Representation Theory and Groups Actions
    • Place of Presentation
      the University of Tokyo, Tokyo
    • Year and Date
      2014-07-12
    • Int'l Joint Research / Invited
  • [Presentation] Visible Actions and Multiplicity-free Representations2014

    • Author(s)
      T. Kobayashi
    • Organizer
      XVIth International Conference on Geometry, Integrability and Quantization
    • Place of Presentation
      Varna, Bulgaria
    • Year and Date
      2014-06-06 – 2014-06-11
    • Int'l Joint Research / Invited
  • [Presentation] Branching problems of representations of real reductive Lie groups2014

    • Author(s)
      T. Kobayashi
    • Organizer
      Representations of reductive groups
    • Place of Presentation
      MIT, USA
    • Year and Date
      2014-05-19 – 2014-05-23
    • Int'l Joint Research / Invited
  • [Presentation] The work of Thurston on Kleinian groups2014

    • Author(s)
      Ken'ichi Ohshika
    • Organizer
      Around Thurston-Grothendieck-Teichmuller theories
    • Place of Presentation
      IRMA, Strasbourg
    • Year and Date
      2014-05-12 – 2014-05-15
    • Int'l Joint Research / Invited
  • [Presentation] The moduli space of pentagons2014

    • Author(s)
      小島定吉
    • Organizer
      NII Shonan Meeting「Knot theory: Algorithms, complexity and computation」
    • Place of Presentation
      湘南国際村センター
    • Year and Date
      2014-04-29
    • Invited

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Published: 2017-01-06  

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