2006/10/31 by Thomas John Baird, Thomas Baird · 39 citations
Mathematics · #Adjoint representation #Advanced Algebra and Geometry #Cohomology #Compact group #Equivariant cohomology #Geometric and Algebraic Topology #Group cohomology #Homotopy and Cohomology in Algebraic Topology #Lie group #Maximal torus #Representation theory #Simple Lie group #math.AT
paper · pdf · doi:10.2140/agt.2007.7.737
published in Algebraic & Geometric Topology 7(2), 737-754 (Mathematical Sciences Publishers) · 11 pages Changes made: Implemented referee recommendations, in particular to use the Vietoris mapping theorem to generalize results and simplify arguments
arxiv created 2007/02/19 · openalex publication_date 2007/05/30 · arxiv updated 2014/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.