2010 Fiscal Year Final Research Report
Study on Geometric group theory
| Project/Area Number |
19340013
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tohoku University |
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Principal Investigator |
FUJIWARA Koji Tohoku University, 大学院・情報科学研究科, 教授 (60229078)
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| Co-Investigator(Renkei-kenkyūsha) |
MORITA Shigeyuki 東京大学, 数理科学研究科, 名誉教授 (70011674)
SHIOYA Takashi 東北大学, 大学院・理学研究科, 教授 (90235507)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 双曲群 / 写像類群 / 擬準同型 / 漸近次元 / 中心極限定理 / カーブグラフ |
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| Research Abstract |
Hyperbolic group was invented by Gromov in 80's. We aim to use hyperbolicity in broader objects. We constructed many quasi-homomorphisms on Kac-Moody groups. We obtained a first finitely presented, simple group with infinite commutator width (with Caprace). Using quasi-homomorphisms, we characterized rank-1 manifolds among complete Riemann manifold of non-positive curvature of finite volume (with Bestvina).
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