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

Details Cohomology of the space of commuting n-tuples in a compact Lie group Cohomology of the space of commuting n-tuples in a compact Lie group

2006-10-25

arxiv.org/abs/math/0610761v3

Algebraic & Geometric Topology 7 (2007) 737-754

Mathematics

Algebraic Topology

11 pages Changes made: Implemented referee recommendations, in particular to use the Vietoris mapping theorem to generalize re

Scientific paper

Consider the space Hom(Z^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(Z^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.

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