Equivariant K-theory of compact Lie group actions with maximal rank isotropy

Abstract

Let G denote a compact connected Lie group with torsion-free fundamental group acting on a compact space X such that all the isotropy subgroups are connected subgroups of maximal rank. Let $T\subset G$ be a maximal torus with Weyl group W. If the fixed-point set $X^T$ has the homotopy type of a finite W-CW complex, we prove that the rationalized complex equivariant K-theory of X is a free module over the representation ring of G. Given additional conditions on the W-action on the fixed-point set $X^T$ we show that the equivariant K-theory of X is free over R(G). We use this to provide computations for a number of examples, including the ordered n-tuples of commuting elements in G with the conjugation action.

Accepted for publication by the Journal of Topology

References in corpus (5)

• Cohomology of the space of commuting n-tuples in a compact Lie group
• Equivariant K-theory of compact Lie group actions with maximal rank isotropy
• Fusion Rings of Loop Group Representations
• Segal's spectral sequence in twisted equivariant K-theory for proper and discrete actions
• On the Structure of the Fusion Ideal

Cited by in corpus (11)

• A classifying space for commutativity in Lie groups
• Equivariant K-theory of compact Lie group actions with maximal rank isotropy
• On spaces of commuting elements in Lie groups
• Hilbert-Poincare series for spaces of commuting elements in Lie groups
• Differentiable stratified groupoids and a de Rham theorem for inertia spaces
• Equivariant formality in $K$-theory
• On the second homotopy group of spaces of commuting elements in Lie groups
• Twisted equivariant K-theory of compact Lie group actions with maximal rank isotropy
• The equivariant K-theory of a cohomogeneity-one action
• Orbifold Euler characteristics of non-orbifold groupoids
• K-theory and formality