Related papers: Surgery and the Spectrum of the Dirac Operator

In presence of string solitons, index theorems for the generalised Dirac operators have to be revisited. We show that in supersymmetric configurations the fermionic operators decouple, so that there are no mixing effects between different…

Suppose $M$ is a closed $n$-dimensional spin$^c$ manifold with spin$^c$ structure $\sigma$ and associated spin$^c$ line bundle $L$. If one fixes a Riemannian metric $g$ on $M$ and a connection $\nabla_L$ on $L$, the generalized scalar…

A supersymmetric theory in two-dimensions has enough data to define a noncommutative space thus making it possible to use all the tools of noncommutative geometry. In particular, we apply this to the N=1 supersymmetric non-linear sigma…

We define the notion of a co-Riemannian structure and show how it can be used to define the Dirac operator on an appropriate infinite dimensional manifold. In particular, this approach works for the smooth loop space of a so-called string…

We construct a universal spin$_c$ Dirac operator on $\mathbb{C}P^n$ built by projecting $su(n+1)$ left actions and prove its equivalence to the standard right action Dirac operator on $\mathbb{C}P^n$. The eigenvalue problem is solved and…

We obtain the spectrum of the Dirac operator on the three-dimensional Heisenberg nilmanifold $\mathcal{M}_3$, and its complete dependence on the metric moduli. As an application, we construct the four-dimensional low-energy effective action…

We construct a natural co-Riemannian structure on the manifold of smooth loops in a Riemannian manifold. We show that the smooth loop space of a string manifold is a per-Hilbert-Schmidt locally equivalent co-spin manifold and thus admits a…

We study boundary value problems for the Dirac operator on Riemannian Spin$^c$ manifolds of bounded geometry and with noncompact boundary. This generalizes a part of the theory of boundary value problems by C. B\"ar and W. Ballmann for…

On complete non-compact manifolds with bounded sectional curvature, we consider a class of self-adjoint Dirac-type operators called Dirac-Schr\"odinger operators. Assuming two Dirac-Schr\"odinger operators coincide at infinity, by previous…

In this paper we consider the Hilbert-Einstein-Dirac functional, whose critical points are pairs, metrics-spinors, that satisfy a system coupling the Riemannian and the spinorial part. Under some assumptions, on the sign of the scalar…

We investigate the leading terms of the spectral action for odd-dimensional Riemannian spin manifolds with the Dirac operator perturbed by a scalar function. We calculate first two Gilkey-de Witt coefficients and make explicit calculations…

For closed manifolds endowed with a Riemannian foliation of codimension $4$, one can define a transversal Seiberg-Witten map. We show that there is a finite dimensional approximation for such a map. By such a method and under the condition…

A signature independent formalism is created and utilized to determine the general second-order symmetry operators for Dirac's equation on two-dimensional Lorentzian spin manifolds. The formalism is used to characterize the orthonormal…

This paper studies geometric structures on noncommutative hypersurfaces within a module-theoretic approach to noncommutative Riemannian (spin) geometry. A construction to induce differential, Riemannian and spinorial structures from a…

The main result of the paper is an extension of the Dirichlet problem from (closures of) bounded open domains U to arbitrary compact subsets X of the complex plane, i.e. the closure of the corresponding space of functions which are harmonic…

We show that for compact Riemannian manifolds of dimension at least $3$ with nonempty boundary, we can modify the manifold by performing surgeries of codimension $2$ or higher, while keeping the Steklov spectrum nearly unchanged. This shows…

The aim of this paper is to study a possible "boundary phenomenon" for Spinc Dirac operators in a special case. If you parametrise Spinc Dirac operators by a family of connections on a Spinc 4-manifold with boundary, this boundary inherits…

We establish the factorization of Dirac operators on Riemannian submersions of compact spin$^c$ manifolds in unbounded KK-theory. More precisely, we show that the Dirac operator on the total space of such a submersion is unitarily…

Index theorems for the Dirac operator allow one to study spinors on manifolds with boundary and torsion. We analyse the modifications of the boundary Chern-Simons correction and APS eta invariant in the presence of torsion. The bulk…

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…