Related papers: Riemann-Roch via deformation quantization, II

We derive gradient and second order {\em a priori} estimates for solutions of the Neumann problem for a general class of fully nonlinear elliptic equations on compact Riemannian manifolds with boundary. These estimates yield regularity and…

Motivated by the work of Cappell, Deturck, Gluch and Miller, we extend the notion of cohomology of harmonic forms (of a compact manifold with boundary) to the abstract setting of Hilbert complexes. Then, we present some geometric…

We derive an integral representation which encodes all coefficients of the Riemann normal coordinate expansion, and also a closed formula for those coefficients.

In this paper, we develop a new approach to the deformation theory of restricted Lie-Rinehart algebras in positive characteristic, based on the deformation theory of restricted morphisms introduced in our earlier work. We provide a full…

We develop the notion of deformations using a valuation ring as ring of coefficients. This permits to consider in particular the classical Gerstenhaber deformations of associative or Lie algebras as infinitesimal deformations and to solve…

Let $M$ be a compact Riemannian manifold endowed with an isometric action of a compact Lie group. The method of the Witten deformation is used to compute the virtual representation-valued equivariant index of a transversally elliptic, first…

We establish integral formulas and sharp two-sided bounds for the Ricci curvature, mean curvature and second fundamental form on a Riemannian manifold with boundary. As applications, sharp gradient and Hessian estimates are derived for the…

We prove a companion forms theorem for mod l Hilbert modular forms. This work generalises results of Gross and Coleman--Voloch for modular forms over Q, and gives a new proof of their results in many cases. The methods used are completely…

A Heisenberg-Clifford realization of a deformed $U(sl_{2})$ by two parameters $p$ and $q$ is discussed. The commutation relations for this deformed algebra have interesting connection with the theta functions.

We generalize the classical de Rham decomposition theorem for Riemannian manifolds to the setting of geodesic metric spaces of finite dimension.

This paper has two parts. The first part is a review and extension of the methods of integration of Leibniz algebras into Lie racks, including as new feature a new way of integrating 2-cocycles (see Lemma 3.9). In the second part, we use…

We give an explicit local formula for any formal deformation quantization, with separation of variables, on a K\"ahler manifold. The formula is given in terms of differential operators, parametrized by acyclic combinatorial graphs.

We consider a smooth groupoid of the form \Sigma\rtimes\Gamma where \Sigma is a Riemann surface and \Gamma a discrete pseudogroup acting on \Sigma by local conformal diffeomorphisms. After defining a K-cycle on the crossed product…

First we establish a weighted Reilly formula for differential forms on a smooth compact oriented Riemannian manifold with boundary. Then we give two applications of this formula when the manifold satisfies certain geometric conditions. One…

We investigate deformations of lagrangian manifolds with singularities. We introduce a complex similar to the de Rham-complex whose cohomology calculates deformation spaces. Examples of singular lagrangian varieties are presented and…

Given a smooth proper dg-algebra $A$, a perfect dg $A$-module $M$, and an endomorphism $f$ of $M$, we define the Hochschild class of the pair $(M,f)$ with values in the Hochschild homology of $A$. Our main result is a Riemann-Roch type…

In this paper, we study quantization on a compact integral symplectic manifold $X$ with transversal real polarizations. In the case of complex polarizations, namely $X$ is K\"ahler equipped with transversal complex polarizations $T^{1, 0}X,…

Pizzetti's formula explicitly shows the equivalence of the rotation invariant integration over a sphere and the action of rotation invariant differential operators. We generalize this idea to the integrals over real, complex, and quaternion…

In the second of a pair of papers, we complete the construction of Seiberg-Witten-like invariants for smooth four-manifolds equipped with broken fibrations, prove an index formula, and compute some examples.

We prove a Riemann-Roch theorem for real divisors on edge-weighted graphs over the reals, extending the result of Baker and Norine for integral divisors on graphs with multiple edges.