2016 Fiscal Year Final Research Report
Cohomology of mapping class groups, Coxeter groups and Artin groups
| Project/Area Number |
26400077
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Hokkaido University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
SATOH Takao 東京理科大学, 理学部第二部, 准教授 (70533256)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | トポロジー / Coxeter群 / Artin群 / 群のコホモロジー / カンドル |
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| Outline of Final Research Achievements |
We studied group cohomology of Coxeter groups, Artin groups and related groups. As for Coxeter groups, we obtain (1) a vanishing theorem for the p-local homology of Coxeter groups (2) a vanishing theorem for the mod p cohomology of alternating subgroups of finite Coxeter groups. As for Artin groups (3) we determined the second mod 2 homology of arbitrary Artin groups. (2) and (3) are joint works with Ye Liu. Finally, we proved that the adjoint group of an arbitrary Coxeter quandle is both a central extension of a Coxeter group W by a free abelian group and a semi-direct product of the commutator subgroup of a Coxeter group W and a free abelian group.
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| Free Research Field |
トポロジー
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