1994 Fiscal Year Final Research Report Summary
Fixed point theorems and cobordism
| Project/Area Number |
05452008
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Osaka University |
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Principal Investigator |
KAWAKUBO Katsuo Osaka Univ.Dept.Math.Professor, 理学部, 教授 (50028198)
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| Co-Investigator(Kenkyū-buntansha) |
KASUE Atsushi Osaka City Univ.Dept.Math.Professor, 理学部, 教授 (40152657)
MURAKAMI Jun Osaka Univ.Dept.Math.Associate Professor, 理学部, 助教授 (90157751)
OZEKI Hideki Osaka Univ.Dept.Math.Professor, 理学部, 教授 (60028082)
MIYANISHI Masayoshi Osaka Univ.Dept.Math.Professor, 理学部, 教授 (80025311)
NAGASAKI Ikumitsu Osaka Univ.Dept.Math.Assistant Professor, 理学部, 講師 (50198305)
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| Project Period (FY) |
1993 – 1994
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| Keywords | Fixed point theorems / Cobordism / Homotopy representation / Burnside ring / Knot / Hecke algebra / Lefschetz ring / Alexander polynomial |
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| Research Abstract |
Kawakubo constructed G-manifolds which are G-s-cobordant, but are not G-homeomorphic for arbitrary compact Lie groups G.Nagasaki computed the structure of the LH groups which are introduced for the purpose of investigating the linearity of homotopy representations of finite groups. As an application, he determined the set of finite groups whose homotopy representations are always linear. Murakami constructed a vertex type state model in Turaev's sense for the multi-variable Alexander polynomial. By using this model, a new set of axioms for the multi-variable Alexander polynomial is obtained. He also determined the structure of the centralizer algebra of the mixed tensor representations of the quantum group U_q (gl (n, c) ). This algebra can be considered as a generalization of the Iwahori Hecke algebra of type A.Using this algebra, he generalized the Yamada polynomial, which is an invariant of embeddings of a spatial graph in S^3. He also investigated representations of the category of tangles using Kontsevich's iterated integral, and succeeded in giving a combinatorial description of Kontsevich's integrals of knots, links and tangles.
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