Related papers: (1,1)-forms acting on Spinors on K\"ahler Surfaces

In this note, we give a geometric expression for the multiplicities of the equivariant index of a Dirac operator twisted by a line bundle.

Operator fields in the bundle of Dirac spinors and their conversion to spatial fields are considered. Some commutator equations are studied with the use of the conversion technique.

We consider Dirac operators on odd-dimensional compact spin manifolds which are twisted by a product bundle. We show that the space of connections on the twisting bundle which yield an invertible operator has infinitely many connected…

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…

We characterize operator-theoretic properties (boundedness, compactness, and Schatten class membership) of Toeplitz operators with positive measure symbols on Bergman spaces of holomorphic hermitian line bundles over K\"ahler…

In this paper, we prove the invariance of the spectrum of the basic Dirac operator defined on a Riemannian foliation $(M,\mathcal{F})$ with respect to a change of bundle-like metric. We then establish new estimates for its eigenvalues on…

Under various elliptic boundary conditions, we obtain lower eigenvalue estimates for Dirac operators by using Hormander's weighted $L^2$-technique. Lower bounds in terms of the volume of the underlying manifolds are also deduced from the…

I begin by explaining how Riemannian geometry can be understood in terms of principal fibre bundles and connections thereon. I then introduce and motivate the definition of a spinor structure in terms of familiar geometrical ideas. The…

In this largely expository paper we give a self-contained treatment of the Dirac operator. Emphasizing the algebraic point of view we first sketch the necessary prerequisites from Clifford algebras and their representations and then define…

We obtain geometric estimates for the first eigenvalue and the fundamental tone of the p-laplacian on manifolds in terms of admissible vector fields. Also, we defined a new spectral invariant and we show its relation with the geometry of…

In this note, we prove lower and upper bounds for Dirac operators of submanifolds in certain ambient manifolds in terms of conformal and extrinsic quantities.

We show that, in round spheres of dimension $n\geq3$, for any given collection of codimension 2 smooth submanifolds $\mathfrak{S}:=\{\Sigma_1,...,\Sigma_N\}$ of arbitrarily complicated topology ($N$ being the complex dimension of the spinor…

We give a description of the image of tensor products of tautological bundles on Hilbert schemes of points on surfaces under the Bridgeland-King-Reid-Haiman equivalence. Using this, some new formulas for cohomological invariants of these…

Since the first work of Thomas Friedrich showing that isometric immersions of Riemann surfaces are related to spinors and the Dirac equation, various works appeared generalizing this approach to more general Spin-manifolds, in particular…

In an earlier paper (math.SG/0101206), we introduced Floer homology theories associated to closed, oriented three-manifolds Y and SpinC structures. In the present paper, we give calculations and study the properties of these invariants. The…

It is shown that on a compact spin symmetric space with a K\"ahler or Quaternion-K\"ahler structure, the first eigenvalue of the Dirac operator is linked to a ''{lowest}'' action of the holonomy, given by the fiberwise action on spinors of…

Twistor forms are a natural generalization of conformal vector fields on Riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We study twistor forms on compact…

In this paper, we establish two kinds of Kastler-Kalau-Walze type theorems for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection on six-dimensional manifolds with boundary.

We examine spectra of Dirac operators on compact hyperbolic surfaces. Particular attention is devoted to symmetry considerations, leading to non-trivial multiplicities of eigenvalues. The relation to spectra of Maass-Laplace operators is…

This expository paper details the theory of rank one Higgs bundles over a closed Riemann surface X and their relationship to representations of the fundamental group of X. We construct an equivalence between the deformation theories of flat…