Related papers: Index of elliptic operators for a diffeomorphism
Indicial operators are model operators associated to an elliptic differential operator near a corner singularity on a stratified manifold. These model operators are defined on generalized tangent cone configurations and exhibit a natural…
We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncompact, but the boundary is assumed to be compact. We require a symmetry property of the principal symbol of the…
A C*algebra A generated by a class of zero-order classical pseudodifferential operator on a cylinder RxB, where B is a compact riemannian manifold, containing operators with periodic symbols, is considered. A description of the K-theory…
If a differential operator $D$ on a smooth Hermitian vector bundle $S$ over a compact manifold $M$ is symmetric, it is essentially self-adjoint and so admits the use of functional calculus. If $D$ is also elliptic, then the Hilbert space of…
For operators belonging either to a class of global bisingular pseudodifferential operators on $R^m \times R^n$ or to a class of bisingular pseudodifferential operators on a product $M \times N$ of two closed smooth manifolds, we show the…
We study elliptic theory on manifolds with boundary represented as a covering space. Firstly, we consider boundary value problems, where the boundary conditions are allowed to mix the values of functions in the fibers of the covering. We…
We show that the index of an elliptic Fourier integral operator associated to a contact diffeomorphism $\phi$ of cosphere bundles of two Riemannian manifolds X and Y is given by $\int_{B^*X}\hat{A}(T^*X)\exp{\theta} -…
In order to study the Toeplitz algebras related to a Dirac operators in a neighborhood of a closed bounded domain D with smooth boundary in C^n we introduce a singular Cauchy type integral. We compute its principal symbol, thus initiating…
For a smooth manifold X of dimension <d we construct a homomorphism from the algebraic K-theory group in degree d of the algebra of smooth functions on X to the degree -d-1 topological K-theory of X with coefficients in C/Z. This map…
In a previous paper we have introduced the gauge-equivariant K-theory group of a bundle endowed with a continuous action of a bundle of compact Lie groups. These groups are the natural range for the analytic index of a family of…
An integer valued topological index of a Dirac operator is introduced for a pair of a 4n+2 dimensional open Spin^c manifold and a section of the determinant line bundle satisfying some property. We show a relation between the index and an…
Boutet de Monvel's calculus provides a pseudodifferential framework which encompasses the classical differential boundary value problems. In an extension of the concept of Lopatinski and Shapiro, it associates to each operator two symbols:…
We present an index theorem for certain hypoelliptic differential operators on foliated manifolds. Our proof is a development of Alain Connes tangent groupoid proof of the Atiyah-Singer index theorem. The paper is largely self-contained.
We consider the operator algebra generated by pseudodifferential operators on a closed smooth surface and shift operator induced by a Morse--Smale diffeomorphism of this surface. Elements in this algebra are considered as operators in the…
We study the relation between spectral flow and index theory within the framework of (unbounded) KK-theory. In particular, we consider a generalised notion of 'Dirac-Schr\"odinger operators', consisting of a self-adjoint elliptic…
On filtered manifolds one can define a different notion of order for the differential operators. In this paper, we use generalized fixed point algebras to construct a pseudodifferential extension that reflects this behaviour. In the…
In previous work, we gave a local formula for the index of Heisenberg elliptic operators on contact manifolds. We constructed a cocycle in periodic cyclic cohomology which, when paired with the Connes-Chern character of the principal…
We study equivariant families of Dirac operators on the source fibers of a Lie groupoid with a closed space of units and equipped with an action of an auxiliary compact Lie group. We use the Getzler rescaling method to derive a fixed-point…
We give a local formula for the index of a transverse Dirac-type operator on a compact manifold with a Riemannian foliation, under the assumption that the Molino sheaf is a sheaf of abelian Lie algebras.
We consider an action of the real line on a C*-algebra for which there is a centre-valued invariant trace. We define a family of Toeplitz operators with symbols in the original algebra. When the symbol is invertible, the Toeplitz operator…