Volume 16, issue 1 (2016)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Classifying spaces of twisted loop groups

Thomas J Baird

Algebraic & Geometric Topology 16 (2016) 211–229
Abstract

We study the classifying space of a twisted loop group LσG, where G is a compact Lie group and σ is an automorphism of G of finite order modulo inner automorphisms. Equivalently, we study the σ–twisted adjoint action of G on itself. We derive a formula for the cohomology ring H(BLσG) and explicitly carry out the calculation for all automorphisms of simple Lie groups. More generally, we derive a formula for the equivariant cohomology of compact Lie group actions with constant rank stabilizers.

Keywords
loop groups, twisted conjugacy, twisted adjoint action, equivariant cohomology, classifying spaces, gauge groups
Mathematical Subject Classification 2010
Primary: 22E67
Secondary: 57S15
References
Publication
Received: 8 May 2014
Revised: 25 May 2015
Accepted: 16 June 2015
Published: 23 February 2016
Authors
Thomas J Baird
Department of Mathematics & Statistics
Memorial University of Newfoundland
St. John’s NF A1C 5S7
Canada
http://www.thomasjohnbaird.com