2019 Fiscal Year Final Research Report
Topological studies on cohomology of Artin groups and related topics
| Project/Area Number |
17K05237
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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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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Keywords | 群のコホモロジー / Coxeter群 / Artin群 / カンドル |
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| Outline of Final Research Achievements |
The adjoint group of a Coxeter quandle is an intermediate group between the corresponding Coxeter group and the Artin group. The study of cohomology of adjoint groups is important for the study of cohomology of Coxeter groups and Artin groups. As results, we determined the rational cohomology rings of all adjoint groups, proved that Hepworth families of adjoint groups have homology stability, and evaluated vanishing ranges of mod p cohomology groups of adjoint groups.
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| Free Research Field |
位相幾何学
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| Academic Significance and Societal Importance of the Research Achievements |
Artin群のコホモロジーがCoxeter群のコホモロジーの1次近似であることから、それらの中間に位置するCoxeterカンドルの随伴群のコホモロジーは、カンドルの理論だけでなくArtin群とCoxeter群のコホモロジーの研究においても重要である。本研究ではCoxeterカンドルの随伴群のホモロジー安定性の証明、コホモロジーの消滅域の評価などにより、Coxeterカンドルのコホモロジーの研究を大きく進展させた。
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