#### Volume 20, issue 5 (2016)

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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