Related papers: Equivariant vector bundles over classifying spaces…

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.…

In a previous paper, we have constructed, for an arbitrary Lie group G and any of the fields F=R or C, a good equivariant cohomology theory KF_G^*(-) on the category of proper $G$-CW-complex and have justified why it deserved the label…

This note gives an overview of the mathematical framework underlying topological insulators, highlighting the connection to K-theory and vector bundles. We see ``real'' and ``quaternionic'' vector bundles arise naturally in the presence of…

The main result of this paper is the $G$-homotopy invariance of the $G$-index of signature operator of proper co-compact $G$-manifolds. If proper co-compact $G$ manifolds $X$ and $Y$ are $G$-homotopy equivalent, then we prove that the…

We prove a finite-dimensional covariant Stinespring theorem for compact quantum groups. Let G be a compact quantum group, and let T:= Rep(G) be the rigid C*-tensor category of finite-dimensional continuous unitary representations of G. Let…

Let $X$ be a complex scheme acted on by an affine algebraic group $G$. We prove that the Atiyah class of a $G$-equivariant perfect complex on $X$, as constructed by Huybrechts and Thomas, is $G$-equivariant in a precise sense. As an…

We introduce and compare two approaches to equivariant homotopy theory in a topological or ordinary Quillen model category. For the topological model category of spaces, we generalize Piacenza's result that the categories of topological…

In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…

We show that every orbispace satisfying certain mild hypotheses has 'enough' vector bundles. It follows that the K-theory of finite rank vector bundles on such orbispaces is a cohomology theory. Global presentation results for smooth…

Consider a proper, isometric action by a unimodular locally compact group $G$ on a Riemannian manifold $M$ with boundary, such that $M/G$ is compact. Then an equivariant Dirac-type operator $D$ on $M$ under a suitable boundary condition has…

For a finite extension $F$ of $\mathbb{Q}_p$ and $n \geq 1$, let $D$ be the division algebra over $F$ of invariant $1/n$ and let $G^0$ be the subgroup of $\text{GL}_n(F)$ of elements with norm $1$ determinant. We show that the action of…

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…

Let $D$ be a (generalized) Dirac operator on a non-compact complete Riemannian manifold $M$ acted on by a compact Lie group $G$. Let $v:M --> Lie(G)$ be an equivariant map, such that the corresponding vector field on $M$ does not vanish…

We show that any continuous $\mathbf{C}$-linear Lie algebra splitting of the symbol map from the Atiyah algebra of a vector bundle on a complex manifold is given by a differential operator of order at most the rank of the bundle plus one.…

This is a further investigation of our approach to group actions in homological algebra in the settings of homology of {\Gamma}-simplicial groups, particularly of {\Gamma}-equivariant homology and cohomology of {\Gamma}-groups. This…

In this article we describe the $G\times G$-equivariant $K$-ring of $X$, where $X$ is a regular compactification of a connected complex reductive algebraic group $G$. Furthermore, in the case when $G$ is a semisimple group of adjoint type,…

Stratified-algebraic vector bundles on real algebraic varieties have many desirable features of algebraic vector bundles but are more flexible. We give a characterization of the compact real algebraic varieties having the following…

We unify problems about the equivariant geometry of symmetric quiver representation varieties, in the finite type setting, with the corresponding problems for symmetric varieties $GL(n)/K$ where $K$ is an orthogonal or symplectic group. In…

We compare the K-theories of symplectic quotients with respect to a compact connected Lie group and with respect to its maximal torus, and in particular we give a method for computing the former in terms of the latter. More specifically,…

Let G be a compact connected Lie group, and (M,\omega) a Hamiltonian G-space with proper moment map \mu. We give a surjectivity result which expresses the K-theory of the symplectic quotient M//G in terms of the equivariant K-theory of the…