2006 Fiscal Year Final Research Report Summary
Research of a boundary of a Coxeter system and dimension theory
| Project/Area Number |
16540067
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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 | Shimane University |
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Principal Investigator |
YOKOI Katsuya Shimane University, Mathematics, Associate Professor, 総合理工学部, 助教授 (90240184)
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| Co-Investigator(Kenkyū-buntansha) |
HOSAKA Tetsuya Utsunomiya University, Mathematics, Associate Professor, 教育学部, 助教授 (50344908)
KIMURA Makoto Shimane University, Mathematics, Professor, 総合理工学部, 教授 (30186332)
HATTORI Yasunao Shimane University, Mathematics, Professor, 総合理工学部, 教授 (20144553)
FURUMOCHI Tetsuo Shimane University, Mathematics, Professor, 総合理工学部, 教授 (40039128)
MAEDA Sadahiro Shimane University, Mathematics, Professor, 総合理工学部, 教授 (40181581)
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| Project Period (FY) |
2004 – 2006
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| Keywords | transitive / graph / Coxeter group / compactness degree / コンパクト指数 |
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| Research Abstract |
We studied :
(K.Yokoi)
1. the relation between transitivity and strong transitivity for graph self-maps,
2. a Barge-Martin type theorem for graph self-maps for which the set of periodic points is dense,
(T.Hosaka)
3. the interior of the limit set of a group acting on a hyperbolic or CAT(0) space,
4. dense subsets of the boundary of a Coxeter groups,
5. Coxeter systems with two-dimensional Davis-Vinberg complexes,
6. strong rigidity and strong reflection rigidity of Coxeter systems of dihedral gropus,
7. boundaries of parabolic subgroups of Coxeter groups,
8. the minimality of the boundary of a Coxeter systems,
9. reflection groups of geodesic spaces,
(M.Kimura)
10. congruent classes of Frenet curves of order 2 in the complex quadric,
11. the possibility of different presentations of spaces as unions or partitions of locally compact subspaces, and
(Y.Hattori)
12. there is no upper bound of small transfinte compactness degree in metrizable spaces.
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