Cohomology of the space of commuting n-tuples in a compact Lie group
By T. Baird. 2006
52 citations recorded by the source corpus.
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. 57S99
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/cde32c4ea17dc8e6d9c47609e8e87bbee24103fe
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Topology of character varieties of Abelian groups (2013, background): “Some special cases of this problem and related questions have recently received attention as can be seen, for example, in the articles [1, 4, 5, 16, 22, 36, 42].”
- Commuting elements, simplicial spaces and filtrations of classifying spaces (2008, background): “Assume that the space Hom(Zn, G) is path–connected, then as was shown in [6], φn is surjective and the fibers of the induced map φn : (G × T n)/N (T ) → Hom(Zn, G) are rationally acyclic.”