## Algebraic & Geometric Topology

### Classifying spaces of twisted loop groups

Thomas J Baird

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 16, Number 1 (2016), 211-229.

Dates
Revised: 25 May 2015
Accepted: 16 June 2015
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.agt/1510841107

Digital Object Identifier
doi:10.2140/agt.2016.16.211

Mathematical Reviews number (MathSciNet)
MR3470700

Zentralblatt MATH identifier
1337.22011

#### Citation

Baird, Thomas J. Classifying spaces of twisted loop groups. Algebr. Geom. Topol. 16 (2016), no. 1, 211--229. doi:10.2140/agt.2016.16.211. https://projecteuclid.org/euclid.agt/1510841107

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