#### Volume 11, issue 1 (2007)

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

### Carles Broto, Ran Levi and Bob Oliver

Geometry & Topology 11 (2007) 315–427
##### 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 ${\left(ℤ∕{p}^{\infty }\right)}^{r}$ 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”.

##### Keywords
classifying space, $p$–completion, fusion, compact Lie groups, $p$–compact groups
##### Mathematical Subject Classification 2000
Primary: 55R35
Secondary: 55R40, 57T10