Related papers: Equivariant eta forms and equivariant differential…

Let $X$ be a smooth compact manifold. We propose a geometric model for the group $K^0(X,\mathbb{R}/\mathbb{Z}).$ We study a well-defined and non-degenerate analytic duality pairing between $K^0(X,\mathbb{R}/\mathbb{Z})$ and its Pontryagin…

We establish a compensated compactness theorem in the microlocal and geometric analytic framework. For a weakly $L^2_{\rm loc}$-convergent sequence of sections of a vector bundle over a semi-Riemannian manifold whose image under a…

In this paper, we first establish a K-theory version of the equivariant family index theorem for a circle action, then use it to prove several rigidity and vanishing theorems on the equivariant K-theory level.

Let G be a finite group. We systematically exploit general homological methods in order to reduce the computation of G-equivariant KK-theory to topological equivariant K-theory. The key observation is that the functor assigning to a…

This paper aims to provide an explicit computation of the equivariant noncommutative residue density of which yield the metric and Einstein tensors on even-dimensional Riemannian manifolds. A considerable contribution of this paper is the…

A duality is discussed for Lie group bundles vs. certain tensor categories with non-simple identity, in the setting of Nistor-Troitsky gauge-equivariant K-theory. As an application, we study C*-algebra bundles with fibre a fixed-point…

We generalise Atiyah and Hirzebruch's vanishing theorem for actions by compact groups on compact Spin-manifolds to possibly noncompact groups acting properly and cocompactly on possibly noncompact Spin-manifolds. As corollaries, we obtain…

Let $G$ be a compact quantum group. We show that given a $G$-equivariant $\mathrm{C}^*$-correspondence $E$, the Pimsner algebra $\mathcal{O}_E$ can be naturally made into a $G$-$\mathrm{C}^*$-algebra. We also provide sufficient conditions…

For a proper, cocompact action by a locally compact group of the form $H \times G$, with $H$ compact, we define an $H \times G$-equivariant index of $H$-transversally elliptic operators, which takes values in $KK_*(C^*H, C^*G)$. This…

In this note, we describe a connection between the enumerative geometry of curves in K3 surfaces and the chiral ring of an auxiliary superconformal field theory. We consider the invariants calculated by Yau--Zaslow (capturing the Euler…

In this paper, we prove a Kastler-Kalau-Walze type theorem for perturbations of Dirac operators on compact manifolds with or without boundary. As a corollary, we give two kinds of operator-theoretic explanations of the gravitational action…

We present an operator-coefficient version of Sato's infinite-dimensional Grassmann manifold, and tau-function. In this context, the Burchnall-Chaundy ring of commuting differential operators becomes a C*-algebra, to which we apply the…

We develop a formula for the equivariant index of a twisted Dirac operator on a compact globally hyperbolic spacetime with timelike boundary on which a group acts isometrically, subject to APS boundary conditions. The formula is the same as…

A. Vistoli proved a decomposition theorem for the rational equivariant algebraic K-theory of a variety under the action of a finite group $G$. We generalize his result to more general algebraic (co)homology theories having the Mackey…

Let $\mathcal{A}_0$ and $\mathcal{A}_1$ be two self-adjoint Fredholm Dirac-type operators defined on two non-compact manifolds. If they coincide at infinity so that the relative heat operator is trace-class, one can define their relative…

We study the equivariant K-group of the affine flag manifold with respect to the Borel group action. We prove that the structure sheaf of the (infinite-dimensional) Schubert variety in the K-group is represented by a unique polynomial,…

In this paper we define K-theoretic secondary invariants attached to a Lie groupoid $G$. The K-theory of $C^*_r(G_{ad}^0)$ (where $G_{ad}^0$ is the adiabatic deformation $G$ restricted to the interval $[0,1)$) is the receptacle for…

Replaces Previous version. Includes comments on poincare duality for twisted equivariant in the context of proper and discrete actions and the Baum-Connes Conjecture. We use a spectral sequence proposed by C. Dwyer and previous work by…

In this paper, we establish a precise connection between higher rho invariants and delocalized eta invariants. Given an element in a discrete group, if its conjugacy class has polynomial growth, then there is a natural trace map on the…

We construct equivariant $KK$-theory with coefficients in $\mathbb{R}$ and $\mathbb{R}/\mathbb{Z}$ as suitable inductive limits over ${\rm II}_1$-factors. We show that the Kasparov product, together with its usual functorial properties,…