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The trace of an action and the degree of a map


Author: Daniel Henry Gottlieb
Journal: Trans. Amer. Math. Soc. 293 (1986), 381-410
MSC: Primary 57S17; Secondary 55M20, 55M25, 55R10, 57S15
DOI: https://doi.org/10.1090/S0002-9947-1986-0814928-9
MathSciNet review: 814928
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Abstract: Two integer invariants of a fibration are defined: the degree, which generalizes the usual notion, and the trace. These numbers represent the smallest transfers for integral homology which can be constructed for the fibrations. Since every action gives rise to a fibration, we have the trace of an action. A list of properties of this trace is developed. This list immediately gives, in a mechanical way, new proofs and generalizations of theorems of Borsuk-Ulam, P. A. Smith, Conner and Floyd, Bredon, W. Browder, and G. Carlsson.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1986-0814928-9
Keywords: Transformation group, transfer, fibre bundle, elementary abelian $ p$-group, Serre spectral sequence
Article copyright: © Copyright 1986 American Mathematical Society

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