The trace of an action and the degree of a map

Gottlieb, Daniel Henry

doi:10.1090/S0002-9947-1986-0814928-9

The trace of an action and the degree of a map
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Trans. Amer. Math. Soc. 293 (1986), 381-410 Request permission

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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