2011 Fiscal Year Final Research Report
Comprehensive studies of topological aspects of algebraic spaces and stratified spaces
| Project/Area Number |
21540088
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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 | Kagoshima University |
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Principal Investigator |
YOKURA Shoji 鹿児島大学, 大学院・理工学研究科, 教授 (60182680)
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| Co-Investigator(Kenkyū-buntansha) |
MIYAJIMA Kimio 鹿児島大学, 大学院・理工学研究科, 教授 (40107850)
AIKOU Tadashi 鹿児島大学, 大学院・理工学研究科, 教授 (00192831)
YASUDA Takehiko 鹿児島大学, 大学院・理工学研究科, 准教授 (30507166)
FURUSAWA Hitoshi 鹿児島大学, 大学院・理工学研究科, 准教授 (00357930)
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| Co-Investigator(Renkei-kenkyūsha) |
OHMOTO Toru 北海道大学, 大学院・理学研究科, 准教授 (20264400)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 代数多様体 / コボルデイズム / モチーフ / 特性類 / bivariant theory / algebraic cobordism / ゼータ関数 |
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| Research Abstract |
(1) Using motivic Hirzebruch class, we constructed Motive Milnor classe, which is a generalization of the Milnor number. (2) W constructed a zeta function of the motivic Hirzebruch class, a special case of which gives rise to the zeta function of the Chern class. (3) Using the idea in the universal bivariant theory introduced by the representative of this grant, we introduced the notion of fiberwise bordism group and we showed that we could construct a bivariant theory of fiberwise bordism group, using the notion of differentiable spaces. (4) We showed that any additive invariant, which cannot be usually captured as a natural transformation, could be captured as a natural transformation.
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