Approximating equivariant mapping spaces

Steven R. Costenoble, Stefan Waner and G. S. Wells

Vol. 144 (1990), No. 1, 15–45

DOI: 10.2140/pjm.1990.144.15

Abstract

Let SV and S^V be the unit sphere and one-point compactification of the unitary representation V of the finite group G. One has the associated self-mapping G-spaces 𝒰(SV,SV ) and Ω^V S^V respectively, the first consisting of unbased maps and the second of based maps. It is the goal of this paper to describe homotopy approximations of these loop spaces (as examples of a more general class of G-spaces), along the lines of the group completion approximations of Segal, McDuff and Hauschild. We then apply these approximations to obtain splittings and Hopf space structures for several spaces.

Mathematical Subject Classification 2000

Primary: 55P91

Secondary: 55R91

Milestones

Received: 29 August 1988

Revised: 25 January 1989

Published: 1 July 1990