Related papers: Equivariant Higher Analytic Torsion and Equivarian…

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…

We show that certain pullbacks of $*$-algebras equivariant with respect to a compact group action remain pullbacks upon completing to $C^*$-algebras. This unifies a number of results in the literature on graph algebras, showing that…

We introduce a Hopf algebroid associated to a proper Lie group action on a smooth manifold. We prove that the cyclic cohomology of this Hopf algebroid is equal to the de Rham cohomology of invariant differential forms. When the action is…

Let a finite set of interacting particles be given, together with a symmetry Lie group $G$. Here we describe all possible dynamics that are jointly equivariant with respect to the action of $G$. This is relevant e.g., when one aims to…

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…

We compute the (primary) equivariant Euler characteristics of the building for the general linear group over a finite field.

We show that for any cohomogeneity one continuous action of a compact connected Lie group $G$ on a closed topological manifold the equivariant cohomology equipped with its canonical $H^*(BG)$-module structure is Cohen-Macaulay. The proof…

We prove that the Euler characteristic of an even-dimensional compact manifold with positive (nonnegative) sectional curvature is positive (nonnegative) provided that the manifold admits an isometric action of a compact Lie group $G$ with…

Let G be a connected compact Lie group acting on a manifold M and let D be a transversally elliptic operator on M. The multiplicity of the index of D is a function on the set of irreducible representations of G. Let T be a maximal torus of…

We extend the main result in the previous paper of Zhang and the author relating the Milnor-Turaev torsion with the complex valued analytic torsion to the equivariant case.

We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L^2 torsions which, unlike the work of…

We construct a global geometric model for complex analytic equivariant elliptic cohomology for all compact Lie groups. Cocycles are specified by functions on the space of fields of the two-dimensional sigma model with background gauge…

Let $X$ be a complex non-singular toric variety, $E$ an equivariant and ample line bundle on $X$. We introduce a new functional $V_\infty$ on the set of smooth, positive and invariant metrics on $E$. We compare $V_\infty$ to some classical…

For closed manifolds with compact Lie group actions, we study Austin-Braam's Morse-theoretic construction of Borel equivariant cohomology using the technique of stabilization. We show that a $C^1$-small equivariant perturbation produces…

The article consists of a survey on analytic and topological torsion. Analytic torsion is defined in terms of the spectrum of the analytic Laplace operator on a Riemannian manifold, whereas topological torsion is defined in terms of a…

We consider a closed odd-dimensional oriented manifold $M$ together with an acyclic flat hermitean vector bundle $\cF$. We form the trivial fibre bundle with fibre $M$ over the manifold of all Riemannian metrics on $M$. It has a natural…

We prove the deformation invariance of the quantum homogeneous spaces of the q-deformation of simply connected simple compact Lie groups over the Poisson-Lie quantum subgroups, in the equivariant KK-theory with respect to the translation…

The paper is based on a talk. Complete exposition is given in "Equivariant Hirzebruch class for singular varieties". Starting from the classical theory we describe Hirzebruch class and the related Todd genus of a complex singular algebraic…

We extend the equivariant holomorphic Morse inequalities of circle actions to cases with torus and non-Abelian group actions on holomorphic vector bundles over Kahler manifolds and show the necessity of the Kahler condition. For torus…

In this paper, for a compact Lie group action,we prove the anomaly formula and the functoriality of the equivariant Bismut-Cheeger eta forms with perturbation operators when the equivariant family index vanishes. In order to prove them, we…