Finite approximations of p–local compact groups

Gonzalez, Alex

doi:10.2140/gt.2016.20.2923

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Finite approximations of $p$–local compact groups

Alex Gonzalez

Geometry & Topology 20 (2016) 2923–2995

DOI: 10.2140/gt.2016.20.2923

Abstract

We show how every $p$ –local compact group can be described as a telescope of $p$ –local finite groups. As a consequence, we deduce several corollaries, such as a stable elements theorem for the mod $p$ cohomology of their classifying spaces, and a generalized Dwyer–Zabrodsky description of certain related mapping spaces.

Keywords

p-local compact group, p-local finite group, colimit, stable elements, mapping space, classifying space, compact Lie groups

Mathematical Subject Classification 2010

Primary: 20D20, 55R35, 55R40

References

Publication

Received: 3 June 2015

Revised: 4 November 2015

Accepted: 5 December 2015

Published: 7 October 2016

Proposed: Jesper Grodal

Seconded: Haynes Miller, Bill Dwyer

Authors

Alex Gonzalez
Department of Mathematics Kansas State University 138 Cardwell Hall Manhattan, KS 66506 United States
http://www.math.ksu.edu/~agondem

Volume 20, issue 5 (2016)