2003 Fiscal Year Final Research Report Summary
Algebraic topology and formal group law
| Project/Area Number |
13440022
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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 | Kyoto University |
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Principal Investigator |
NISHIDA Goro Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00027377)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAJIMA Hiraku Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00201666)
KONO Akira Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00093237)
FUKAYA Kenji Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (30165261)
TANABE Michimasa Kyoto Univ., Graduate School of Science, Assistant, 大学院・理学研究科, 助手 (20236665)
YOSHIDA Hiroyuki Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (40108973)
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| Project Period (FY) |
2001 – 2003
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| Keywords | cohomnmgv / Hopf algebra / homotopy group / category |
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| Research Abstract |
In Heisei 13, we studied mainly the stable splitting, of Unitary groups given by H. Miller, and considerd its refinment. The homology of Unitary groups are the exterior algebras. Miller's splitting correspond to the degreewise splitting of the exterior algebra. On the other. hand, local splitting at a prime p was given by using the Adams operation. We have shown that we can mix these splittings and obtainned the finner splitting. In Heisei 14, we studied the Mittchell-Priddy spectrum and its cohomology. We found a minimal set of generators as the module over the Steenrod algebra. In Heisei 15, we made two different stdies. One is the study of the structure of Steenrod algebra from a new point of view. The Hopf algebra structure of the Steenrod algebra was determined by Milnor and known the same as the automorphism group of the additive group law. It was not known the conceptional exposition of this fact. We gave this by combining notions of multiplicative operations and the Dickson invariants. The other study is homotopy theory of higher dimensional category. Correspondence between discrete categories and spaces with non-trivial homotopy group in dim 1 is extended to 2 categories
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