Volume 20, issue 5 (2016)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Finite approximations of $p$–local compact groups

Alex Gonzalez

Geometry & Topology 20 (2016) 2923–2995
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