2013 Fiscal Year Final Research Report
Study of intersections and links on non-simply-connected equivariant manifolds and K-theory
| Project/Area Number |
22540085
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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 | Okayama University |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 幾何学 / トポロジー / 多様体 / 絡みと交差 / K-理論 / 変換群 |
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| Research Abstract |
Let G be a finite group, and let X and Y be smooth G-manifolds. Given a G-map f from X to Y, there is an algebraic element (obstruction class) which determines whether one can convert f to a homotopy equivalence g by G-surgeries on X. In this research, considering links (resp. intersections) between elements of the k-th homotopy group of X and (k-1)-dimensional (resp. k-dimensional) H-fixed point sets of X for subgroups H of G, we gave a G-surgery theory to delete /insert fixed point sets in X. As applications of it, we construct various and many new pairs of Smith-equivalent real G-representation spaces.
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