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

Adem, Alejandro; Cantarero, José; Gómez, José Manuel

doi:10.1063/1.5036647

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

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Gómez, José Manuel
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1063/1.5036647
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Citation

Adem, A., Cantarero, J., & Gómez, J. M. (2018). Twisted equivariant K-theory of compact Lie group actions with maximal rank isotropy. Journal of Mathematical Physics, 59(11): 113502. doi:10.1063/1.5036647.

Cite as: https://hdl.handle.net/21.11116/0000-0003-C412-B

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 $G$. Specifically, 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
$Y=\{*\}$.