Related papers: An index theorem on asymptotically static spacetim…

We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by…

Let $M$ be a globally hyperbolic manifold with complete spacelike Cauchy hypersurface $\Sigma \subset M$. Building on past and recent works of B\"ar and Strohmaier, we extend their Fredholm result of the Atiyah-Singer Dirac operator on…

On a compact globally hyperbolic Lorentzian spin manifold with smooth spacelike Cauchy boundary the (hyperbolic) Dirac operator is known to be Fredholm when Atiyah-Patodi-Singer boundary conditions are imposed. In this paper we investigate…

Let $M$ be a temporal compact globally hyperbolic manifold with Cauchy hypersurface $\Sigma$ which is a Galois covering with respect to a discrete group $\Gamma$ of automorphisms such that the quotient $\Sigma/\Gamma$ is compact without…

We consider a hyperbolic Dirac-type operator with growing potential on a a spatially non-compact globally hyperbolic manifold. We show that the Atiyah-Patodi-Singer boundary value problem for such operator is Fredholm and obtain a formula…

A Dirac operator on a complete manifold is Fredholm if it is invertible outside a compact set. Assuming a compact group to act on all relevant structure, and the manifold to have a warped product structure outside such a compact set, we…

We extend the Atiyah, Patodi, and Singer index theorem for first order differential operators from the context of manifolds with cylindrical ends to manifolds with periodic ends. This theorem provides a natural complement to Taubes'…

An equality between the spectral flow of a family $A$ of self-adjoint Fredholm operators and the index of the associated differential operator $\frac{d}{dt}-iA$ with Atiyah-Patodi-Singer-style boundary conditions is shown. This generalizes…

Index theory for Lorentzian Dirac operators is a young subject with significant differences to elliptic index theory. It is based on microlocal analysis instead of standard elliptic theory and one of the main features is that a nontrivial…

We consider the massive Klein-Gordon equation on asymptotically Minkowski spacetimes, in the sense that the manifold is $R^{1+d}$ and the metric approaches that of Minkowski space at infinity in a short-range way (jointly in time and space…

Let $M$ be a globally hyperbolic manifold with complete spacelike Cauchy hypersurface $\Sigma$. We prove well-posedness of the Cauchy problem for the Dirac operator on globally hyperbolic manifolds with complete Cauchy hypersurfaces. This…

We give a self-contained proof of a formula computing the Fredholm index for asymptotically non-degenerate Cauchy-Riemann operators on surfaces with boundary punctures using the method of large antilinear deformations. This method for…

We derive a formula for the index of a Dirac operator on a compact, even-dimensional incomplete edge space satisfying a "geometric Witt condition". We accomplish this by cutting off to a smooth manifold with boundary, applying the…

We study an example of an index problem for a Dirac-like operator subject to Atiyah-Patodi-Singer boundary conditions on a noncommutative manifold with boundary, namely the quantum unit disk.

We establish an $L^2$-Gamma index theorem for the Dirac operator on a globally hyperbolic manifold $M$ with Cauchy hypersurface $\Sigma$ being a Galois covering of a compact smooth manifold with Galois group $\Gamma$. Our argument rewrites…

Non-local boundary conditions, such as the Atiyah-Patodi-Singer (APS) conditions, for Dirac operators on Riemannian manifolds are well understood while not much is known for such operators on spacetimes with timelike boundary. We define a…

We present the details of our embedding proof of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary.

In this paper, we consider the eigenvalue problem of Dirac operator on a compact Riemannian manifold isometrically immersed into Euclidean space and derive some extrinsic estimates for the sum of arbitrary consecutive $n$ eigenvalues of the…

We extend the relative index theorem on non-compact manifolds to encompass a wide variety of hypoelliptic differential operators of arbitrary order, demonstrating that the change in index when changing a differential operator locally can be…

We consider the index of a Dirac operator on a compact even dimensional manifold with a domain wall. The latter is defined as a co-dimension one submanifold where the connection jumps. We formulate and prove an analog of the…