Related papers: Fibered cusp versus $d$- index theory

On a n-dimensional connected compact manifold with non-empty boundary equipped with a Riemannian metric, a spin structure and a chirality operator, we study some properties of a spin conformal invariant defined from the first eigenvalue of…

We derive a general obstruction to the existence of Riemannian metrics of positive scalar curvature on closed spin manifolds in terms of hypersurfaces of codimension two. The proof is based on coarse index theory for Dirac operators that…

We give a formulation of a deformation of Dirac operator along orbits of a group action on a possibly non-compact manifold to get an equivariant index and a K-homology cycle representing the index. We apply this framework to non-compact…

Let $M$ be a spin manifold, the Dirac operator with coefficient in the universal flat Hilbert $C^\ast \pi_1(M)$-module determines a "Rosenberg index element" which, according to B.Hanke and T.Schick, subsumes the enlargeablility obstruction…

In this paper, we give two Lichnerowicz type formulas for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection. We also prove two Kastler-Kalau-Walze type theorems for twisted Dirac operators and…

The Hochschild and cyclic homology groups are computed for the algebra of `cusp' pseudodifferential operators on any compact manifold with boundary. The index functional for this algebra is interpreted as a Hochschild 1-cocycle and…

The endoscopic transfer factor is expressed as difference of characters for the even and odd parts of the spin modules, or Dirac index of the trivial representation. The lifting of tempered characters in terms of index of Dirac cohomology…

In this expository paper, we explain a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a $G$-manifold. The formula is a sum of integrals over blowups of the strata of the group action and…

We construct the coarse index class with support condition (as an element of coarse $K$-homology) of an equivariant Dirac operator on a complete Riemannian manifold endowed with a proper, isometric action of a group. We further show a…

Let M be a compact manifold with a fixed spin structure \chi. The Atiyah-Singer index theorem implies that for any metric g on M the dimension of the kernel of the Dirac operator is bounded from below by a topological quantity depending…

We give a min-max characterization of the weighted Dirac eigenvalues, and show that the weighted eigenvalues and eigenspaces of Dirac operators are continuous with respect to weak $L^p$ convergence of the inverse weight, for any $p>n$.…

A manifold with fibered cusp metrics $X$ can be considered as a geometrical generalization of locally symmetric spaces of $\mathbb{Q}$-rank one at infinity. We prove a Hodge-type theorem for this class of Riemannian manifolds, i.e. we find…

The fermionic topological charge of lattice gauge fields, given in terms of a spectral flow of the Hermitian Wilson--Dirac operator, or equivalently, as the index of Neuberger's lattice Dirac operator, is shown to have analogous properties…

The aim of the lectures is to introduce first-year Ph.D. students and research workers to the theory of the Dirac operator, spinor techniques, and their relevance for the theory of eigenvalues in Riemannian geometry. Topics: differential…

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…

This paper reviews some recent work on (s)pin structures and the Dirac operator on hypersurfaces (in particular, on spheres), on real projective spaces and quadrics. Two approaches to spinor fields on manifolds are compared. The action of…

We consider the Dirac operator on asymptotically static Lorentzian manifolds with an odd-dimensional compact Cauchy surface. We prove that if Atiyah-Patodi-Singer boundary conditions are imposed at infinite times then the Dirac operator is…

We consider the magnetic Dirac operator on a curved strip whose boundary carries the infinite mass boundary condition. When the magnetic field is large, we provide the reader with accurate estimates of the essential and discrete spectra. In…

We announce a Godbillon-Vey index formula for longitudinal Dirac operators on a foliated bundle $(X,\F)$ with boundary; in particular, we define a Godbillon-Vey eta invariant on the boundary foliation, that is, a secondary invariant for…

We investigate the spectrum of the spin Dirac operator on families of hyperbolic surfaces where a set of disjoint simple geodesics shrink to $0$, under the hypothesis that the spin structure is non-trivial along each pinched geodesic. The…