2016 Fiscal Year Final Research Report
Research on spaces of non-positive curvature, their isometry groups and Coxeter groups
| Project/Area Number |
25800039
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Shizuoka University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | 幾何学的群論 / 位相幾何学 / グラフ理論 |
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| Outline of Final Research Achievements |
I obtained some results on CAT(0) groups, CAT(0) spaces, their boundaries, Coxeter groups and graph theory. First, in the case that a group acts geometrically (i.e. cocompactly, properly discontinuously and by isometries) on two proper CAT(0) spaces, I gave a sufficient condition and an equivalent condition of the group actions as there exists an equivariant homeomorphism between the ideal boundaries of the two CAT(0) spaces. In particular, I obtained some results in the case that the CAT(0) group is a Coxeter group. By observing some applications and examples, I obtained a conjecture that some CAT(0) groups with some simple forms will be non-boundary-rigid CAT(0) groups with uncountable many boundaries. Also I obtained some results on reconstructible graphs from investigating corresponding Coxeter groups.
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| Free Research Field |
幾何学
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