## Geometry & Topology

### Discrete models for the $p$–local homotopy theory of compact Lie groups and $p$–compact groups

#### Abstract

We define and study a certain class of spaces which includes $p$–completed classifying spaces of compact Lie groups, classifying spaces of $p$–compact groups, and $p$–completed classifying spaces of certain locally finite discrete groups. These spaces are determined by fusion and linking systems over “discrete $p$–toral groups”—extensions of $(ℤ∕p∞)r$ by finite $p$–groups—in the same way that classifying spaces of $p$–local finite groups as defined in our paper [The homotopy theory of fusion systems, J. Amer. Math. Soc. 16 (2003) 779–856] are determined by fusion and linking systems over finite $p$–groups. We call these structures “$p$–local compact groups”.

#### Article information

Source
Geom. Topol., Volume 11, Number 1 (2007), 315-427.

Dates
Accepted: 20 November 2006
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513799836

Digital Object Identifier
doi:10.2140/gt.2007.11.315

Mathematical Reviews number (MathSciNet)
MR2302494

Zentralblatt MATH identifier
1135.55008

#### Citation

Broto, Carles; Levi, Ran; Oliver, Bob. Discrete models for the $p$–local homotopy theory of compact Lie groups and $p$–compact groups. Geom. Topol. 11 (2007), no. 1, 315--427. doi:10.2140/gt.2007.11.315. https://projecteuclid.org/euclid.gt/1513799836

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