Algebraic & Geometric Topology

Cohomology of the space of commuting $n$–tuples in a compact Lie group

Thomas John Baird

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Consider the space Hom(n,G) of pairwise commuting n–tuples of elements in a compact Lie group G. This forms a real algebraic variety, which is generally singular. In this paper, we construct a desingularization of the generic component of Hom(n,G), which allows us to derive formulas for its ordinary and equivariant cohomology in terms of the Lie algebra of a maximal torus in G and the action of the Weyl group. This is an application of a general theorem concerning G–spaces for which every element is fixed by a maximal torus.

Article information

Algebr. Geom. Topol., Volume 7, Number 2 (2007), 737-754.

Received: 21 November 2006
Revised: 13 February 2007
Accepted: 22 March 2007
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 57S99: None of the above, but in this section

Lie groups cohomology


Baird, Thomas John. Cohomology of the space of commuting $n$–tuples in a compact Lie group. Algebr. Geom. Topol. 7 (2007), no. 2, 737--754. doi:10.2140/agt.2007.7.737.

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