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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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 幾何学的群論 / 位相幾何学 / CAT(0)空間 / CAT(0)群 / Coxeter群 / Davis複体 / 境界 / 再構成可能グラフ / flag complex / quasi-isometry / equivariant同相 / equivariant 同相 / asymptotic次元 / Higson corona / 次元 |
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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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Report
(5 results)
Research Products
(27 results)
