Related papers: The K-theory of the conjugation action

The goal of the present paper is the calculation of the equivariant twisted K-theory of a compact Lie group which acts on itself by conjugations, and elements of a TQFT-structure on the twisted K-groups. These results are originally due to…

Using a global version of the equivariant Chern character, we describe the complexified twisted equivariant K-theory of a space with a compact Lie group action in terms of fixed-point data. We apply this to the case of a compact Lie group…

For a compact simply connected simple Lie group $G$ with an involution $\alpha$, we compute the $G\rtimes \Z/2$-equivariant K-theory of $G$ where $G$ acts by conjugation and $\Z/2$ acts either by $\alpha$ or by $g\mapsto \alpha(g)^{-1}$. We…

For T an abelian compact Lie group, we give a description of T-equivariant K-theory with complex coefficients in terms of equivariant cohomology. In the appendix we give applications of this by extending results of Chang-Skjelbred and…

Let $G$ be a compact, connected, and simply-connected Lie group, equipped with a Lie group involution $\sigma_G$ and viewed as a $G$-space with the conjugation action. In this paper, we present a description of the ring structure of the…

Let $G$ be a compact, connected, and simply-connected Lie group, equipped with an anti-involution $a_G$ which is the composition of a Lie group involutive automorphism $\sigma_G$ and the group inversion. We view $(G, a_G)$ as a Real $(G,…

We compute the equivariant complex K-theory ring of a cohomogeneity-one action of a compact Lie group at the level of generators and relations and derive a characterization of K-theoretic equivariant formality for these actions. Less…

In this paper we study a natural decomposition of $G$-equivariant $K$-theory of a proper $G$-space, when $G$ is a Lie group with a compact normal subgroup $A$ acting trivially. Our decomposition could be understood as a generalization of…

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.…

We compute the equivariant $K$-theory $K_G^*(G)$ for a simply connected Lie group $G$ (acting on itself by conjugation). We prove that $K_G^*(G)$ is isomorphic to the algebra of Grothendieck differentials on the representation ring. We also…

This is the first in a series of papers investigating the relationship between the twisted equivariant K-theory of a compact Lie group G and the "Verlinde ring" of its loop group. In this paper we set up the foundations of twisted…

The smooth action of a compact Lie group on a compact manifold can be resolved to an iterated space, as made explicit by Pierre Albin and the second author. On the resolution the lifted action has fixed isotropy type, in an iterated sense,…

In joint work with M. Hopkins and C. Teleman we find a new description of the Verlinde algebra associated to a compact Lie group. In this expository account we describe twisted K-theory, prove the theorem for the group SU(2), and motivate…

In this note we present an analogue of equivariant formality in $K$-theory and show that it is equivalent to equivariant formality \emph{\`a la} Goresky-Kottwitz-MacPherson. We also apply this analogue to give alternative proofs of…

Twisted complex $K$-theory can be defined for a space $X$ equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C$^*$-algebras. Up to equivalence, the twisting corresponds to an element of $H^3(X;\Z)$. We…

This note surveys the well-known structure of G-manifolds and summarizes parts of two papers that have not yet appeared in print: one with joint with J. Bruning and F. W. Kamber, and another with I. Prokhorenkov. In particular, from a given…

Using an equivariant version of Connes' Thom Isomorphism,w}e prove that equivariant $K$-theory is invariant under strict deformation quantization for a compact Lie group action.

In this paper, extending the results in \cite{F}, we compute Adams operations on twisted $K$-theory of connected, simply-connected and simple compact Lie groups $G$, in both equivariant and nonequivariant settings.

This is the second in a series of papers investigating the relationship between the twisted equivariant K-theory of a compact Lie group G and the "Verlinde ring" of its loop group. We introduce the Dirac family of Fredholm operators…

We compute the equivariant $K$-homology of the classifying space for proper actions, for compact 3-dimensional hyperbolic reflection groups. This coincides with the topological $K$-theory of the reduced $C^\ast$-algebra associated to the…