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2007 Cohomology of the space of commuting $n$–tuples in a compact Lie group
Thomas John Baird
Algebr. Geom. Topol. 7(2): 737-754 (2007). DOI: 10.2140/agt.2007.7.737

Abstract

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.

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Thomas John Baird. "Cohomology of the space of commuting $n$–tuples in a compact Lie group." Algebr. Geom. Topol. 7 (2) 737 - 754, 2007. https://doi.org/10.2140/agt.2007.7.737

Information

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

zbMATH: 1163.57026
MathSciNet: MR2308962
Digital Object Identifier: 10.2140/agt.2007.7.737

Subjects:
Primary: 57S99

Keywords: Cohomology, Lie groups

Rights: Copyright © 2007 Mathematical Sciences Publishers

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