2012 Fiscal Year Final Research Report
Research on spaces of non-positive curvature with group actions and Coxeter groups
| Project/Area Number |
21740037
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Shizuoka University (2011-2012)
Utsunomiya University (2009-2010) |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2012
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| Keywords | 幾何学的群論 / 位相幾何学 |
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| Research Abstract |
I have obtained some results on CAT(0) groups, CAT(0) spaces, their boundaries and Coxeter groups. First, I proved a "splitting theorem" for CAT(0) spaces, and obtained that products of rigid CAT(0) groups are also rigid CAT(0). Next, I had some results on equivariant-homeomorphisms of boundaries of CAT(0) groups. Also I obtained results on algebraic rigidity of Coxeter groups and on graph theory by investigating corresponding Coxeter groups.
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