2011 Fiscal Year Final Research Report
Coho mology of discrete groups and characteristic classes of flat bundles
| Project/Area Number |
20340008
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Hokkaido University |
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Principal Investigator |
AKITA Toshiyuki 北海道大学, 大学院・理学研究院, 准教授 (30279252)
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| Co-Investigator(Kenkyū-buntansha) |
OHMOTO Toru 北海道大学, 大学院・理学研究院, 准教授 (20264400)
WATANABE Tadayuki 北海道大学, 大学院・理学研究院, 助教 (70467447)
YOSHIDA Tomoyuki 北海道大学, 大学院・理学研究院, 教授 (30002265)
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| Co-Investigator(Renkei-kenkyūsha) |
KURIBAYASHI Katsuhiko 信州大学, 理学部, 教授 (40249751)
YAGITA Nobuaki 茨城大学, 教育学部, 教授 (20130768)
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| Project Period (FY) |
2008 – 2011
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| Keywords | コホモロジー / 特性類 / 線型表現 / 写像類群 / 分岐被覆 |
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| Research Abstract |
We construct a functorial framework to deal with all finite transformation groups on closed surfaces (Galois covers on closed surfaces) simultaneously. Characteristic classes associated with such transformation groups, Mumford-Morita-Miller classes and Newton classes, are shown to be natural transformations of functors. These characteristic classes are shown to satisfy Riemann-Roch type formulae.
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