The Transfer Map and Fiber Bundles

Abstract

LETS: E + B be a fiber bundle whose fiber Fis a compact smooth manifold, whose structure group G is a compact Lie group acting smoothly on F, and whose base B is a finite complex. Let x denote the Euler characteristic of F. It is shown in [12] that there exists a “transfer” homomorphism Q: H*(E) + H*(B) with the property that the composite @* is multiplication by II. The main purpose of this paper is to construct an Smap T: B+ + E+ which induces the homomorphism Q (+ denoting disjoint union with a base point). We call r the transfer associated with the fiber bundle p: E + B. In the case of a finite covering space T agrees with the transfer defined by Roush [22] and by Kahn and Priddy [18].

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@inproceedings{Becker1975TheTM, title={The Transfer Map and Fiber Bundles}, author={James C. Becker and Daniel H. Gottlieb}, year={1975} }