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

Abstract

We consider twisted equivariant K--theory for actions of a compact Lie group $G$ on a space $X$ where all the isotropy subgroups are connected and of maximal rank. We show that the associated rational spectral sequence à la Segal has a simple $E_2$--term expressible as invariants under the Weyl group of $G$. Namely, if $T$ is a maximal torus of $G$, they are invariants of the ${\pi }_1(X^T)$-equivariant Bredon cohomology of the universal cover of $X^T$ with suitable coefficients. In the case of the inertia stack $\Lambda Y$ this term can be expressed using the cohomology of $Y^T$ and algebraic invariants associated to the Lie group and the twisting. A number of calculations are provided. In particular, we recover the rational Verlinde algebra when $Y=\{\ast \}$.

To appear in Journal of Mathematical Physics. Some mistakes have been corrected in Section 2

References in corpus (1)

• Segal's spectral sequence in twisted equivariant K-theory for proper and discrete actions

Cited by in corpus (2)

• Equivariant higher twisted K-theory of SU(n) for exponential functor twists
• Spectral Sequence Computation of Higher Twisted $K$-Groups of $SU(n)$