Classifying spaces for 1–truncated compact Lie groups

Rezk, Charles

doi:10.2140/agt.2018.18.525

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Classifying spaces for $1$–truncated compact Lie groups

Charles Rezk

Algebraic & Geometric Topology 18 (2018) 525–546

DOI: 10.2140/agt.2018.18.525

Abstract

A $1$ –truncated compact Lie group is any extension of a finite group by a torus. In this note we compute the homotopy types of ${Map}_{*} (B G, B H)$ , $Map (B G, B H)$ , and $Map (E G, B_{G} H)$ for compact Lie groups $G$ and $H$ with $H$ $1$ –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.

Keywords

classifying spaces, equivariant

Mathematical Subject Classification 2010

Primary: 55R91

Secondary: 55P92, 55R35, 55R37

References

Publication

Received: 2 February 2017

Revised: 30 June 2017

Accepted: 18 July 2017

Published: 10 January 2018

Authors

Charles Rezk
Department of Mathematics University of Illinois Urbana, IL United States
http://www.math.illinois.edu/~rezk

Volume 18, issue 1 (2018)