2000 Fiscal Year Final Research Report Summary
Deformation of algobras and S^1-action
| Project/Area Number |
11640087
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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 | University of the Ryukyus |
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Principal Investigator |
SHIGA Hiroo College of Science, University of the Ryukyus Professor, 理学部, 教授 (40128484)
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| Co-Investigator(Kenkyū-buntansha) |
TSUKUDA Shuichi College of Science, University of the Ryukyus Research assistant, 理学部, 助手 (50305182)
TEZUKA Michisige College of Science, University of the Ryukyus Professor, 理学部, 教授 (20197784)
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| Project Period (FY) |
1999 – 2000
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| Keywords | rational fibration / deformation of algebra / S^1-action / forgetful map |
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| Research Abstract |
Let X be a complex on which S^1 acts. The cohomology ring of X is obtained by the deformation of the cohomology ring of the fixed points set. We classify the ring which appear as a cohomology ring of fixed points sets when dim_Q H^X (X : Q) ≦5, Let X be a ratinal elliptic homotopy type with positive Euler characteristic. When dim_Q H^X (X : Q) ≦7, we completed the classification. Let X be a complex X on which S^1 acts freely. We studied the kernel of the forgetfull map. F : Aut^1X→AutX.We find examples when kerF is a finite group, infinitely countable group and uncountable group, respectively. We also give the condition that kerF is a finite group.
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