• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Relatively hyperbolic structures of groups

Research Project

Project/Area Number 15K17534
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionYokohama National University

Principal Investigator

Yamagagta Saeko  横浜国立大学, 教育学部, 准教授 (70513563)

Project Period (FY) 2015-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords相対的双曲群 / 相対的擬凸部分群 / 相対的双曲構造 / 普遍相対的双曲構造 / 幾何学 / 離散群
Outline of Final Research Achievements

Let G be a group which is not necessarily countable. Let H and K be two families of subgroups of G. Assume that each subgroup which belongs to K is contained in some subgroup which belongs to H.
In this research, we discuss relations of relative hyperbolicity for the group G with respect to the two families H and K, respectively. If the group G is hyperbolic relative to H and K, respectively, then we consider relations of relative quasiconvexity for a subgroup L of the group G with respect to H and K, respectively.

Academic Significance and Societal Importance of the Research Achievements

相対的双曲性をもつ群に関するこれまでの世界的な研究の流れとしては, 1つの相対的双曲構造(RHS)に着目して, その群の性質を調べるというものが大部分であった. また, グロモフの双曲群に対して成り立つ定理が, 相対的双曲性をもつ群に対しても一般化できるか, という方針の下での結果が大部分であった.
そんな中,「与えられた群に対し, その群のRHS全体に着目する.」「部分群の包含関係から決まる自然な半順序を, その群のRHS全体からなる集合に入れる.」という着想に基づく本研究は, 相対的双曲性をもつ群に対し, グロモフの双曲群の単なる一般化を超えた新しい意味づけを与えている.

Report

(6 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (4 results)

All 2019 2018 2015

All Journal Article (4 results) (of which Peer Reviewed: 4 results)

  • [Journal Article] On Relative Hyperbolicity for a Group and Relative Quasiconvexity for a Subgroup2019

    • Author(s)
      MATSUDA Yoshifumi、OGUNI Shin-ichi、YAMAGATA Saeko
    • Journal Title

      Tokyo Journal of Mathematics

      Volume: 42 Issue: 1 Pages: 83-112

    • DOI

      10.3836/tjm/1502179263

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Relative Hyperbolicity for a Group and Relative Quasiconvexity for a Subgroup2019

    • Author(s)
      Yoshifumi MATSUDA, Shin-ichi OGUNI, and Saeko YAMAGATA
    • Journal Title

      Tokyo J. Math.

      Volume: 早期公開

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] On relative hyperbolicity for a group and relative quasiconvexity for a subgroup2018

    • Author(s)
      Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata
    • Journal Title

      Tokyo Journal of Mathematics

      Volume: 印刷中

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Notes on relatively hyperbolic groups and relatively quasiconvex subgroups2015

    • Author(s)
      Yoshifumi MATSUDA, Shin-ichi OGUNI, and Saeko YAMAGATA
    • Journal Title

      Tokyo Journal of Mathematics

      Volume: 38 Pages: 99-123

    • Related Report
      2015 Research-status Report
    • Peer Reviewed

URL: 

Published: 2015-04-16   Modified: 2022-11-04  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi