2013 Fiscal Year Final Research Report
Constructions of cocycles of finite groups by characteristic classes
| Project/Area Number |
23654018
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Hokkaido University |
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Principal Investigator |
AKITA Toshiyuki 北海道大学, 理学(系)研究科(研究院), 准教授 (30279252)
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| Co-Investigator(Renkei-kenkyūsha) |
HASHIMOTO Yoshitake 東京都市大学, 知識工学部, 教授 (20271182)
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| Project Period (FY) |
2011 – 2013
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| Keywords | コサイクル / 特性類 / 群のコホモロジー / Galois被覆 / Coxeter群 |
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| Research Abstract |
For a finite Galois covering of a compact Riemann surface with a monodromy group G, we constructed cocycles representing the characteristic classes (Mumford-Morita-Miller classes) associated with a Galois covering, by using transfer homomorphisms in group cohomology and Kawazumi-Uemura formula. In addition, we construct mod p cocycles for such classes by using "periodicity phenomena" and Steenrod operations. Moreover, we prove a vanishing theorem for p-local homology of Coxeter groups. The key ingredient was equivariant homology of Coxeter complexes.
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Research Products
(14 results)
