2013 Fiscal Year Final Research Report
Coarse analyzing metric spaces of non-positive curvature and topological analyzing remainders of its compactifications
| Project/Area Number |
22540105
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | 防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工学群) (2012-2013)
Hiroshima Institute of Technology (2010-2011) |
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Principal Investigator |
CHINEN NAOTSUGU 防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工, 総合教育学群, 教授 (20370067)
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| Co-Investigator(Kenkyū-buntansha) |
TOMOYASU Kazuo 都城工業高等専門学校, その他部局等, 准教授 (10332107)
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| Co-Investigator(Renkei-kenkyūsha) |
KOYAMA Akira 早稲田大学, 理工学術院, 教授 (40116158)
HOSAKA Tetsuya 静岡大学, 理学(系)研究科(研究院), 准教授 (50344908)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 位相幾何 / 幾何学的群論 / コクセター群 / 写像によるカラーリング / asymptotic次元 / Coarse 幾何学 / 距離に依存するコンパクト化 / Higsonコンパクト化 |
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| Research Abstract |
It is important mathematically (in particular, geometrically) to study Coxeter groups. We investigate Coxeter groups and obtain topological properties for boundaries of metric spaces of non-positive curvature and hyperbolic spaces on whose Coxeter groups are geometrically acted. Specifically, we provide the following results: a necessary and sufficient condition with a topological fractal structure of its boundary, the construction of topological universal spaces as the boundaries of Coxeter groups, and, an extension of the decomposition theorem to the Coxeter group. Moreover, we investigate colorings numbers of maps deeply related to fix points of remainders of compactifications and we obtain a necessary and sufficient condition with colorings numbers of homeomorphisms on locally finite graphs.
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