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

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(BG,BH), Map(BG,BH), and Map(EG,BG 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.

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classifying spaces, equivariant
Mathematical Subject Classification 2010
Primary: 55R91
Secondary: 55P92, 55R35, 55R37
Received: 2 February 2017
Revised: 30 June 2017
Accepted: 18 July 2017
Published: 10 January 2018
Charles Rezk
Department of Mathematics
University of Illinois
Urbana, IL
United States