#### Volume 18, issue 1 (2018)

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Classifying spaces for $1$–truncated compact Lie groups

### Charles Rezk

Algebraic & Geometric Topology 18 (2018) 525–546
##### Abstract

A $1\phantom{\rule{0.3em}{0ex}}$–truncated compact Lie group is any extension of a finite group by a torus. In this note we compute the homotopy types of ${Map}_{\ast }\left(BG,BH\right)$, $Map\left(BG,BH\right)$, and $Map\left(EG,{B}_{G}H\right)$ for compact Lie groups $G$ and $H$ with $H$ $1\phantom{\rule{0.3em}{0ex}}$–truncated, showing that they are computed entirely in terms of spaces of homomorphisms from $G$ to $H$. These results generalize the well-known case when $H$ is finite, and the case when $H$ is compact abelian due to Lashof, May, and Segal.

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##### Keywords
classifying spaces, equivariant
##### Mathematical Subject Classification 2010
Primary: 55R91
Secondary: 55P92, 55R35, 55R37