Algebraic & Geometric Topology

Classifying spaces of twisted loop groups

Thomas J Baird

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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