Relatively hyperbolic structures of groups
Project/Area Number |
15K17534
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Geometry
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Research Institution | Yokohama National University |
Principal Investigator |
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Project Period (FY) |
2015-04-01 – 2020-03-31
|
Project Status |
Completed (Fiscal Year 2019)
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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)
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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.
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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.
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Report
(6 results)
Research Products
(4 results)