Cohomology of the space of commuting \(n\)-tuples in a compact Lie group (Q2464769)

The space \(\mathrm{Hom}(\mathbb{Z}^n,G)\) of pairwise commuting \(n\)-tuples of elements in a compact Lie group \(G\) forms a generally singular real algebraic variety. The author constructs a desingularization of the generic component of \(\mathrm{Hom}(\mathbb{Z}^n,G)\). This desingularization is applied to derive formulas for the ordinary and equivariant cohomology of \(\mathrm{Hom}(\mathbb{Z}^n,G)\).