Classifying spaces of twisted loop groups

Baird, Thomas J

doi:10.2140/agt.2016.16.211

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Classifying spaces of twisted loop groups

Thomas J Baird

Algebraic & Geometric Topology 16 (2016) 211–229

DOI: 10.2140/agt.2016.16.211

Abstract

We study the classifying space of a twisted loop group $L_{σ} G$ , 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 $H^{*} (B L_{σ} G)$ 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

Volume 16, issue 1 (2016)