Algebraic & Geometric Topology

Classifying spaces of twisted loop groups

Thomas J Baird

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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
Received: 8 May 2014
Revised: 25 May 2015
Accepted: 16 June 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
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

Subjects
Primary: 22E67: Loop groups and related constructions, group-theoretic treatment [See also 58D05]
Secondary: 57S15: Compact Lie groups of differentiable transformations

Keywords
loop groups twisted conjugacy twisted adjoint action equivariant cohomology classifying spaces gauge groups

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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