Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57S17, 55M20, 55M25, 55R10, 57S15

Retrieve articles in all journals with MSC: 57S17, 55M20, 55M25, 55R10, 57S15


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