# Item

ITEM ACTIONSEXPORT

Released

Journal Article

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

##### External Resource

https://doi.org/10.1063/1.5036647

(Publisher version)

##### Fulltext (restricted access)

There are currently no full texts shared for your IP range.

##### Fulltext (public)

arXiv:1709.00989.pdf

(Preprint), 400KB

##### Supplementary Material (public)

There is no public supplementary material available

##### 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

$Y=\{*\}$.

$Y=\{*\}$.