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Various aspects of rigidity problems

Research Project

Project/Area Number 17204004
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionNagoya University

Principal Investigator

KANAI Masahiko  Nagoya University, 大学院・多元数理科学研究科, 教授 (70183035)

Co-Investigator(Kenkyū-buntansha) 井関 裕靖  東北大学, 大学院・理学研究科, 助教授 (90244409)
太田 啓史  名古屋大学, 大学院・多元数理科学研究科, 教授 (50223839)
小林 俊行  東京大学, 大学院・数理科学研究科, 教授 (80201490)
坪井 俊  東京大学, 大学院・数理科学研究科, 教授 (40114566)
藤原 耕二  東北大学, 大学院・研究科, 教授 (60229078)
Co-Investigator(Renkei-kenkyūsha) IZEKI Hiroyasu  東北大学, 大学院・理学研究科, 准教授 (90244409)
OHTA Hiroshi  名古屋大学, 大学院・多元数理科学研究科, 教授 (50223839)
KOBAYASHI Toshiyuki  東京大学, 大学院・数理科学研究科, 教授 (80201490)
KONDO Shigeyuki  名古屋大学, 大学院・多元数理科学研究科, 教授 (50186847)
TSUBOI Takashi  東京大学, 大学院・数理科学研究科, 教授 (40114566)
NAYATANI Shin  名古屋大学, 大学院・多元数理科学研究科, 教授 (70222180)
FUJIWARA Koji  東北大学, 大学院・情報学研究科, 教授 (60229078)
MATSUMOTO Shigenori  日本大学, 理工学部, 教授 (80060143)
Project Period (FY) 2005 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥26,000,000 (Direct Cost: ¥20,000,000、Indirect Cost: ¥6,000,000)
Fiscal Year 2008: ¥7,280,000 (Direct Cost: ¥5,600,000、Indirect Cost: ¥1,680,000)
Fiscal Year 2007: ¥5,460,000 (Direct Cost: ¥4,200,000、Indirect Cost: ¥1,260,000)
Fiscal Year 2006: ¥6,630,000 (Direct Cost: ¥5,100,000、Indirect Cost: ¥1,530,000)
Fiscal Year 2005: ¥6,630,000 (Direct Cost: ¥5,100,000、Indirect Cost: ¥1,530,000)
Keywords剛性 / 非コンパクト半単純リー群 / 剛性問題 / 非コンパクト半単純高階リー群 / Weyl chamber流 / 松島の消滅定理 / Weilの消滅定理 / 葉層構造の無限小剛性 / 調和写像と剛性 / ランダム群 / フレアコホモロジーの障害・変形理論 / リー群の離散部部分群 / half transvectionで生成される群 / 微分同相群の完全性 / 擬準同型
Research Abstract

研究代表者金井は, 高階非コンパクト半単純リー群およびその余コンパクト格子に付随して現れるワイル領域流 (Weyl chamber flow) の剛性とヴェイユや松島の古典的な消滅定理の間に予期せぬ関係があることを指摘する新たな結果を得た. 剛性問題に新たな進展をもたらすことが期待される. このほかにも, 連携研究者等により剛性問題に対る新たな知見が多数得られた

Report

(5 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (58 results)

All 2009 2008 2007 2006 2005 Other

All Journal Article (31 results) (of which Peer Reviewed: 19 results) Presentation (26 results) Book (1 results)

  • [Journal Article] Rigidity of the Weyl chamber flow, and the classical vanishing theorems of Weil and Matsushima2008

    • Author(s)
      Kanai, Masahiko
    • Journal Title

      Representation theory and analysis on homogeneous spaces, 25-28, RIMS Kokyuroku Bessatsu, B7, Res. Inst. Math. Sci. (RIMS), Kyoto

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Examples of isolated surface singularities whose links have infinitely many symplectic fillings2008

    • Author(s)
      Ohta, Hiroshi and Ono, Kaoru
    • Journal Title

      J. Fixed Point Theory Appl no. 1

      Pages: 51-56

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Rigidity and deformation of discontinuous groups for non-Riemannian symmetric spaces2008

    • Author(s)
      Kobayashi, T
    • Journal Title

      Representation theory and analysis on homogeneous spaces, 1--12, RIMS Kokyuroku Bessatsu, B7, Res. Inst. Math. Sci. (RIMS), Kyoto

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Codimension one minimal foliations and the fundamental groups of leaves2008

    • Author(s)
      Yokoyama, Tomoo and Tsuboi, Takashi
    • Journal Title

      Ann. Inst. Fourier (Grenoble) 58 no. 2

      Pages: 723-731

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] The asymptotic dimension of a curve graph is finite2008

    • Author(s)
      Bell, Gregory C. and Fujiwara, Koji
    • Journal Title

      J. Lond. Math. Soc (2)77 no.1

      Pages: 33-50

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Quasi-homomorphisms on mapping class groups2007

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

      Glas. Mat. Ser 42(62) no.1

      Pages: 213-236

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A note on spaces of asymptotic dimension one2007

    • Author(s)
      Fujiwara, Koji and Whyte, Kevin
    • Journal Title

      Algebr. Geom. Topol 7

      Pages: 1063-1070

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Integral formula of the unitary inversion operator for the minimal representation of O(p,q)2007

    • Author(s)
      T.Kobayashi, G.Mano
    • Journal Title

      Proc. Japan Acad. Ser. A 83(3)

      Pages: 27-31

    • NAID

      40015348844

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Deformation of properly discontinuous actions of Z^k on R^{k+1}2006

    • Author(s)
      Kobayashi, Toshiyuki and Nasrin, Salma
    • Journal Title

      Internat. J. Math 17 no.10

      Pages: 1175-1193

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Maximal subgroups of the Mathieu group M_{23} and symplectic automorphisms of supersingular K3 surfaces2006

    • Author(s)
      Kondo, Shigeyuki
    • Journal Title

      Int. Math. Res. Not Art. ID 71517

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the group of foliation preserving diffeomorphisms2006

    • Author(s)
      Tsuboi, Takashi
    • Journal Title

      Foliations 2005, 411-430, World Sci. Publ., Hackensack, NJ

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] JSJ-decompositions of finitely presented groups and complexes of groups2006

    • Author(s)
      Fujiwara, K. and Papasoglu, P
    • Journal Title

      Geom. Funct. Anal 16 no. 1

      Pages: 70-125

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Rigidity of locally free Lie group actions and leafwise cohomology2006

    • Author(s)
      Matsumoto, Shigenori
    • Journal Title

      (Japanese) Sugaku 58 no.1

      Pages: 86-101

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the group of foliation preserving diffeomorphisms2006

    • Author(s)
      Takashi Tsuboi
    • Journal Title

      Foliations 2005, Lodz, World Scientific, Singapore

      Pages: 411-430

    • Related Report
      2006 Annual Research Report
  • [Journal Article] JSJ-decompositions of finitely presented groups and complexes of groups2006

    • Author(s)
      K.Fujiwara, P.Papasoglu
    • Journal Title

      Geometric and Functional Analysis 16

      Pages: 70-125

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Fixed point sets of parabolic isometries of CAT(0)-spaces2006

    • Author(s)
      K.Fujiwara, K.Nagano, T.Shioya
    • Journal Title

      Comm.Math.Helv. 81

      Pages: 305-335

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Deformation of properly discontinuous actions of Z^k on R^<k+1>2006

    • Author(s)
      T.Kobayashi, S.Nasrin
    • Journal Title

      Internat. J. Math. 17

      Pages: 1175-1193

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Maximal subgroups of the Mathieu group M_<23> and symplectic automorphisms of supersingular K3 surfaces2006

    • Author(s)
      Shigeyuki Kondo
    • Journal Title

      International Mathematics Research Notices 2006

      Pages: 1-9

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Compact Clifford-Klein forms of symmetric spaces-revisited2005

    • Author(s)
      Kobayashi, Toshiyuki and Yoshino, Taro
    • Journal Title

      Pure Appl. Math. Q 1 no.3, part 2,

      Pages: 591-663

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Simple singularities and symplectic fillings2005

    • Author(s)
      Ohta, Hiroshi and Ono, Kaoru
    • Journal Title

      J. Diff. Geom 69 no.1

      Pages: 1-42

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Symplectic 4-manifolds containing singular rational curves with (2, 3)-cusp2005

    • Author(s)
      Ohta, Hiroshi and Ono, Kaoru
    • Journal Title

      Singularities Franco-Japonaises, 233-241, Semin. Congr., 10, Soc. Math. France, Paris

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Combinatorial harmonic maps and discrete-group actions on Hadamard spaces2005

    • Author(s)
      Izeki, Hiroyasu and Nayatani, Shin
    • Journal Title

      Geom. Dedicata 114

      Pages: 147-188

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] complex ball uniformization of the moduli space of cubic surfaces via periods of K3 surfaces2005

    • Author(s)
      Dolgachev, I., van Geemen, B. and Kondo, S
    • Journal Title

      J. Reine Angew. Math 588

      Pages: 99-148

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Ends of leaves of Lie foliations2005

    • Author(s)
      Hector, Gilbert, Matsumoto, Shigenori and Meigniez, Gael
    • Journal Title

      J. Math. Soc. Japan 57 no.3

      Pages: 753-779

    • NAID

      10017177824

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Combinatorial harmonic maps and discrete-group actions on Hadamard spaces,2005

    • Author(s)
      IZEKI, Hiroyasu, NAYATANI, Shin
    • Journal Title

      Geom.Dedicata 114

      Pages: 147-188

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Simple singularities and symplectic fillings2005

    • Author(s)
      OHTA, Hiroshi, ONO Kaoru
    • Journal Title

      J.Differential Geom. 69

      Pages: 1-42

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Compact Clifford-Klein forms of symmetric spaces -revisited2005

    • Author(s)
      KOBAYASHI Toshiyuki, YOSHINO Taro
    • Journal Title

      Pure and Applied Mathematics Quarterly 1

      Pages: 603-684

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Group generated by half transvections2005

    • Author(s)
      TSUBOI Takashi
    • Journal Title

      Kodai Math.J. 28

      Pages: 463-482

    • NAID

      130003574505

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On non-bounded generation of discrete subgroups in rank-1 Lie group2005

    • Author(s)
      FUJIWARA, Koji
    • Journal Title

      in "Geometry, spectral theory, groups, and dynamics", Contemp.Math., Amer.Math.Soc. 387

      Pages: 153-156

    • Related Report
      2005 Annual Research Report
  • [Journal Article] 非リーマン等質空間の不連続群について2005

    • Author(s)
      小林俊行
    • Journal Title

      数学 57

      Pages: 267-281

    • NAID

      10017177173

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Rigidity of the Weyl chamber flow

    • Author(s)
      Kanai, Masahiko
    • Journal Title

      and vanishing theorems of Matsushima and Weil, Ergod. Th. Dynam. Sys (に掲載決定済み)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Presentation] 偶数次元多様体の微分同相群の一様完全性2009

    • Author(s)
      坪井俊
    • Organizer
      「同相群とその周辺」研究会
    • Year and Date
      2009-02-21
    • Related Report
      2008 Final Research Report
  • [Presentation] Fundamental Groups of Locally Complex Symmetric Spaces-An Application of Symmetries of Nilpotent Orbits2009

    • Author(s)
      KOBAYASHI, Toshiyuki
    • Organizer
      The 8th Workshop on Nilpotent Orbits and Representation Theory (NORTh 8)
    • Place of Presentation
      Otsu, Japan
    • Related Report
      2008 Final Research Report
  • [Presentation] Global Geometry and Analysis on Locally Symmetric Spaces-Beyond the Riemannian case2009

    • Author(s)
      KOBAYASHI, Toshiyuki
    • Organizer
      Conference in honor of Toshio Oshima's 60th birthday'Differential Equations and Symmetric Spaces
    • Place of Presentation
      University of Tokyo
    • Related Report
      2008 Final Research Report
  • [Presentation] 「安定交換子長についての最近の話題」研究集会2008

    • Author(s)
      松元重則
    • Organizer
      微分同相群と葉層構造
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2008-10-29
    • Related Report
      2008 Final Research Report
  • [Presentation] 多様体の微分同相群2008

    • Author(s)
      坪井俊
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-25
    • Related Report
      2008 Final Research Report
  • [Presentation] A fixed-point property of discrete groups and energy of equivariant maps2008

    • Author(s)
      井関裕靖
    • Organizer
      1st MSJ-SI Probabilistic Approach to Geometry
    • Place of Presentation
      於 京都大学
    • Year and Date
      2008-08-05
    • Related Report
      2008 Final Research Report
  • [Presentation] 微分同相群の一様完全性について2008

    • Author(s)
      坪井俊
    • Organizer
      「同相群とその周辺」研究会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2008-02-19
    • Related Report
      2008 Final Research Report
  • [Presentation] Global Geometry on Locally Symmetric Spaces-beyond the Riemannian case2008

    • Author(s)
      KOBAYASHI, Toshiyuki
    • Organizer
      Representations of Lie groups and applications, Institut Henri
    • Place of Presentation
      Poincare, Paris, France
    • Related Report
      2008 Final Research Report
  • [Presentation] Combable functions and the central limit theorem2008

    • Author(s)
      Fujiwara, Koji
    • Organizer
      Oberwolfach, Geometric Group Theory, Hyperbolic Dynamics and Symplecticm Geometry
    • Place of Presentation
      Germany
    • Related Report
      2008 Final Research Report
  • [Presentation] On the group of real analytic diffeomorphisms, Foliations2007

    • Author(s)
      TSUBOI, Takashi
    • Organizer
      Topology and Geometry in Rio, PUC-Rio
    • Place of Presentation
      Brazil
    • Year and Date
      2007-08-10
    • Related Report
      2008 Final Research Report
  • [Presentation] Rigidity of the Weyl chamber flow, and the vanishing theorems of Weil and Matsushima2007

    • Author(s)
      KANAI, Masahiko
    • Organizer
      International Conference "Spectral Analysis in Geometry and Number Theory"
    • Place of Presentation
      Nagoya, Japan
    • Year and Date
      2007-08-06
    • Related Report
      2008 Final Research Report
  • [Presentation] 固定点性質と同変写像のエネルギー2007

    • Author(s)
      井関裕靖
    • Organizer
      RIMS共同研究「離散群と作用素環論」
    • Place of Presentation
      於京都大学数理解析研究所
    • Year and Date
      2007-01-09
    • Related Report
      2008 Final Research Report
  • [Presentation] 実解析的微分同相の規格化補題2006

    • Author(s)
      坪井俊
    • Organizer
      「同相群とその周辺」研究会
    • Place of Presentation
      京都工芸繊維大学
    • Year and Date
      2006-12-23
    • Related Report
      2008 Final Research Report
  • [Presentation] Fixed-point property of discrete groups2006

    • Author(s)
      井関裕靖
    • Organizer
      研究集会「大域解析と微分幾何-その情報科学への関わり-」
    • Place of Presentation
      於東北大学大学院情報科学研究科
    • Year and Date
      2006-10-22
    • Related Report
      2008 Final Research Report
  • [Presentation] ランダム群に対する固定点定理2006

    • Author(s)
      井関裕靖
    • Organizer
      第49回函数論シンポジウム
    • Year and Date
      2006-09-15
    • Related Report
      2008 Final Research Report
  • [Presentation] On the group of real analytic diffeomorphisms2006

    • Author(s)
      TSUBOI, Takashi
    • Organizer
      Groups of Diffeomorphisms 2006
    • Place of Presentation
      東大数理
    • Year and Date
      2006-09-12
    • Related Report
      2008 Final Research Report
  • [Presentation] On the perfectness of the group of real analytic diffeomorphisms2006

    • Author(s)
      TSUBOI, Takashi
    • Organizer
      ICM2006
    • Place of Presentation
      Madrid
    • Year and Date
      2006-08-24
    • Related Report
      2008 Final Research Report
  • [Presentation] "Weyl chamber flow" の剛性とWeil・松島による古典的な消滅定理2006

    • Author(s)
      金井雅彦
    • Organizer
      表現論シンポジウム
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2006-08-22
    • Related Report
      2008 Final Research Report
  • [Presentation] Stable commutator length on mapping class groups2006

    • Author(s)
      Fujiwara, Koji
    • Organizer
      In "Geometric group theory, dynamical system, and symplectic geometry"
    • Place of Presentation
      Oberwolfach
    • Year and Date
      2006-07-28
    • Related Report
      2008 Final Research Report
  • [Presentation] On the group of real analytic diffeomorphisms2006

    • Author(s)
      坪井俊
    • Organizer
      Tambara Workshop on Holomorphic Foliations and Holomorphic Curves
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2006-05-27
    • Related Report
      2008 Final Research Report
  • [Presentation] 曲面のカーブグラフの幾何, 日本数学会年会2006

    • Author(s)
      藤原耕二
    • Organizer
      幾何学分科会特別講演
    • Place of Presentation
      中央大
    • Year and Date
      2006-03-27
    • Related Report
      2008 Final Research Report
  • [Presentation] On Compact Locally Symmetric Spaces2006

    • Author(s)
      KOBAYASHI, Toshiyuki
    • Organizer
      International Conference on Harmonic Analysis and Applications
    • Place of Presentation
      Sousse, Tunisia
    • Related Report
      2008 Final Research Report
  • [Presentation] On Compact Locally Symmetric Spaces2006

    • Author(s)
      KOBAYASHI, Toshiyuki
    • Organizer
      RIMS Workshop on Representation Theory and Analysis on Homogeneous Spaces (organized by Hideko Sekiguchi)
    • Place of Presentation
      RIMS, Kyoto University, Japan
    • Related Report
      2008 Final Research Report
  • [Presentation] Vanishing Theorems in Geometry and Rigidity of Dynamical Systems2005

    • Author(s)
      KANAI, Masahiko
    • Organizer
      日中幾何学研究集会
    • Place of Presentation
      於唐津
    • Year and Date
      2005-12-23
    • Related Report
      2008 Final Research Report
  • [Presentation] A fixed-point theorem for discrete-group actions on Hadamard spaces2005

    • Author(s)
      井関裕靖
    • Organizer
      一般・幾何学的トポロジーと幾何学的群論研究集会
    • Place of Presentation
      於京都大学数理解析研究所
    • Year and Date
      2005-10-12
    • Related Report
      2008 Final Research Report
  • [Presentation] Infinitesimal rigidity of the Weyl chamber flow via the vanishing theorem of Weil

    • Author(s)
      KANAI, Masahiko
    • Organizer
      July 23-29, 2006,"Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry"
    • Place of Presentation
      Oberwolfach, Germany
    • Related Report
      2008 Final Research Report
  • [Book] リー群と表現論2005

    • Author(s)
      小林俊行, 大島利雄
    • Total Pages
      610
    • Publisher
      岩波書店
    • Related Report
      2005 Annual Research Report

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Published: 2005-04-01   Modified: 2016-04-21  

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