Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 7, Number 2 (2007), 737-754.
Cohomology of the space of commuting $n$–tuples in a compact Lie group
Consider the space of pairwise commuting –tuples of elements in a compact Lie group . This forms a real algebraic variety, which is generally singular. In this paper, we construct a desingularization of the generic component of , which allows us to derive formulas for its ordinary and equivariant cohomology in terms of the Lie algebra of a maximal torus in and the action of the Weyl group. This is an application of a general theorem concerning –spaces for which every element is fixed by a maximal torus.
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
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. https://projecteuclid.org/euclid.agt/1513796703