Geodesic
Cohomology of the space of commuting n–tuples in a compact Lie group
Baird, Thomas John1
1Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada
Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 737-754
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Consider the space Hom(ℤn,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(ℤn,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.

DOI : 10.2140/agt.2007.7.737
Keywords: Lie groups, cohomology

Baird, Thomas John  1

1 Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada 
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Baird, Thomas John. Cohomology of the space of commuting n–tuples in a compact Lie group. Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 737-754. doi: 10.2140/agt.2007.7.737

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