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Research on rigidity of foliations and group actions based on characteristic classes

Research Project

Project/Area Number 26800047
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionRitsumeikan University

Principal Investigator

Nozawa Hiraku  立命館大学, 理工学部, 准教授 (80706557)

Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords微分位相幾何 / 葉層構造 / 特性類 / 剛性理論 / 対称空間 / 局所化 / 佐々木幾何 / 群作用 / 微分位相幾何学 / 二次特性類 / 離散群 / 剛性 / Chern-Simons不変量 / Lie群作用 / 位相幾何国際情報交換フランスドイツブラジル / 葉層構造国際情報交換フランスドイツブラジル / 剛性 国際情報交換(フランス) / 佐々木多様体 国際情報交換(ドイツ、ブラジル) / 特性類 国際情報交換(ドイツ、ブラジル)
Outline of Final Research Achievements

I investigated on foliations, which are geometric structures on spaces detemined by a decomposition of the space to lower dimensional spaces. The first main result of this project is obtained in a collaboration with G. Meigniez (University of South Bourtagne): We proved that Lie foliations with locally symmetric leaves are homogeneous. We applied this result to prove certain rigidity of Riemannian foliations. The second main result of this project is obtained in a collaboration with O. Goertsches (Marburg University) and D. Toben (Federal University of San Carlos). We showed a Atiyah-Bott-Berline-Vergne type localization formula for characteristic classes of Killing foliations to calculate the volume of Sasakian manifolds. We also obtained some results on characteristic classes of Kahler foliations and certain foliations on the unit tangent bundle of hyperbolic manifolds.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (23 results)

All 2017 2016 2015 2014 Other

All Int'l Joint Research (8 results) Journal Article (1 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 1 results,  Acknowledgement Compliant: 1 results) Presentation (13 results) (of which Int'l Joint Research: 3 results,  Invited: 3 results) Remarks (1 results)

  • [Int'l Joint Research] 南ブルターニュ大学(フランス)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] サンティアゴ=デ=コンポステラ大学(スペイン)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] マルブルグ大学(ドイツ)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] サンカルロス連邦大学(ブラジル)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] 南ブルターニュ大学(フランス)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] サンティアゴ=デ=コンポステラ大学(スペイン)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] ルートヴィヒ・マクシミリアン大学ミュンヘン(ドイツ)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] サンカルロス連邦大学(ブラジル)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Localization of Chern-Simons type invariants of Riemannian foliations2017

    • Author(s)
      Oliver Goertsches, Dirk Toben, Hiraku Nozawa
    • Journal Title

      Israel Journal of Mathematics

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] Topology of Sasakian manifolds and torus actions2016

    • Author(s)
      Oliver Goertsches, 野澤 啓, Dirk Toben
    • Organizer
      第43回 変換群論シンポジウム
    • Place of Presentation
      姫路市市民会館(兵庫県姫路市)
    • Year and Date
      2016-11-18
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] ケーラー葉層構造の特性類の変形について2016

    • Author(s)
      野澤 啓
    • Organizer
      葉層構造と微分同相群2016
    • Place of Presentation
      東京大学玉原国際セミナーハウス(群馬県沼田市)
    • Year and Date
      2016-10-20
    • Related Report
      2016 Annual Research Report
  • [Presentation] Independent variation of secondary characteristic classes of Riemannian foliations2016

    • Author(s)
      野澤 啓
    • Organizer
      Foliations 2016
    • Place of Presentation
      Research and Conference Centre in Bedlewo (Poland)
    • Year and Date
      2016-07-16
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] (G,X)-葉層構造の剛性と特性類について2016

    • Author(s)
      野澤啓, Jesus Antonio Alvarez lopez, Gael Meigniez
    • Organizer
      2016年日本数学会年会 幾何学分科会特別講演
    • Place of Presentation
      筑波大学(茨城県つくば市)
    • Year and Date
      2016-03-17
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] 葉層構造の二次特性類の有限的側面について I, II2015

    • Author(s)
      野澤啓, Jesus Antonio Alvarez lopez,
    • Organizer
      幾何学阿蘇研究集会
    • Place of Presentation
      休暇村 南阿蘇(熊本県阿蘇郡高森町)
    • Year and Date
      2015-09-25
    • Related Report
      2015 Research-status Report
  • [Presentation] Property (T) and local rigidity of Riemannian foliations2015

    • Author(s)
      野澤啓
    • Organizer
      Group actions and metric embeddings
    • Place of Presentation
      京都大学(京都府京都市)
    • Year and Date
      2015-09-09
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] ケーラー葉層の二次特性類の変形について2015

    • Author(s)
      野澤 啓
    • Organizer
      研究集会「接触構造、特異点、微分方程式及びその周辺」
    • Place of Presentation
      北海道旭川市市民ときわホール
    • Year and Date
      2015-01-22
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Lie葉層構造の剛性について2014

    • Author(s)
      Gael Meigniez, 野澤 啓
    • Organizer
      京都大学 微分トポロジーセミナー
    • Place of Presentation
      京都大学理学部(京都府)
    • Year and Date
      2014-10-28
    • Related Report
      2014 Research-status Report
  • [Presentation] Riemann葉層の剛性2014

    • Author(s)
      Gael Meigniez, 野澤 啓
    • Organizer
      研究集会「葉層構造と微分同相群 2014」
    • Place of Presentation
      東京大学玉原国際セミナーハウス(群馬県)
    • Year and Date
      2014-10-20
    • Related Report
      2014 Research-status Report
  • [Presentation] Riemann葉層のChern-Simons型不変量の局所化2014

    • Author(s)
      Oliver Goertsches, 野澤 啓, Dirk Toben
    • Organizer
      日本数学会 2014年度秋季総合分科会
    • Place of Presentation
      広島大学東広島キャンパス(広島県)
    • Year and Date
      2014-09-27
    • Related Report
      2014 Research-status Report
  • [Presentation] Rigidity of Riemannian foliations with locally symmetric leaves2014

    • Author(s)
      Gael Meigniez, 野澤 啓
    • Organizer
      Workshop Geometry and Dynamics of Foliations
    • Place of Presentation
      Instituto de Ciencias Matematicas (マドリッド,スペイン)
    • Year and Date
      2014-09-02
    • Related Report
      2014 Research-status Report
  • [Presentation] Lie 葉層の剛性について2014

    • Author(s)
      Gael Meigniez, 野澤 啓
    • Organizer
      第61回幾何学シンポジウム
    • Place of Presentation
      名城大学(愛知県)
    • Year and Date
      2014-08-24
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Lie葉層の剛性について2014

    • Author(s)
      Gael Meigniez, 野澤 啓
    • Organizer
      東京大学幾何コロキウム
    • Place of Presentation
      東京大学数理科学研究科(東京都)
    • Year and Date
      2014-04-24
    • Related Report
      2014 Research-status Report
  • [Remarks] 葉層構造とは

    • URL

      http://www.ritsumei.ac.jp/~hnozawa/jp/seika.html

    • Related Report
      2016 Annual Research Report

URL: 

Published: 2014-04-04   Modified: 2018-03-22  

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