Geometry & Topology

Finite approximations of $p$–local compact groups

Alex Gonzalez

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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.

Article information

Geom. Topol., Volume 20, Number 5 (2016), 2923-2995.

Received: 3 June 2015
Revised: 4 November 2015
Accepted: 5 December 2015
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20D20: Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure 55R35: Classifying spaces of groups and $H$-spaces 55R40: Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20]

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


Gonzalez, Alex. Finite approximations of $p$–local compact groups. Geom. Topol. 20 (2016), no. 5, 2923--2995. doi:10.2140/gt.2016.20.2923.

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