arXiv subjects
Publications and source records attributed to R. Nest.
We identify the 2-groupoid of deformations of a gerbe on a smooth manifold with the Deligne 2-groupoid of a corresponding twist of the DGLA of local Hochschild cochains on infinite jets of smooth functions.
This is the first in a series of articles devoted to deformation quantization of gerbes. Here we give basic definitions and interpret deformations of a given gerbe as Maurer-Cartan elements of a differential graded Lie algebra (DGLA). We classify all deformations of a given gerbe on a symplectic manifold, as well as provide a deformation-theoretic interpretation of the first Rozansky-Witten class.
In this paper we compute the deformation theory of a special class of algebras, namely of Azumaya algebras on a manifold ($C^{\infty}$ or complex analytic).
We consider the norm closure $A$ of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a manifold $X$ with boundary $Y$. We first describe the image and the kernel of the continuous extension of the boundary principal symbol to $A$. If the $X$ is connected and $Y$ is not empty, we then show that the K-groups of $A$ are topologically determined. In case the manifold, its boundary and the tangent space of the interior have torsion-free K-theory, we prove that $K_i(A/K)$ is isomorphic to the direct sum of $K_i(C(X))$ and $K_{1-i}(C_0(TX'))$, for i=0,1, with $K$ denoting the compact ideal and $TX'$ the tangent bundle of the interior of $X$. Using Boutet de Monvel's index theorem, we also prove this result for i=1 without assuming the torsion-free hypothesis. We also give a composition sequence for $A$.
We study the variational equations for solitons in noncommutative scalar field theories in an even number of spatial dimensions. We prove the existence of spherically symmetric solutions for a sufficiently large noncommutativity parameter $θ$ and we prove the absence of spherically symmetric solutions for small $θ$.
We deduce the Riemann-Roch type formula expressing the microlocal Euler class of a perfect complex of D-modules in terms of the Chern character of the associated symbol complex and the Todd class of the manifold from the Riemann-Roch type theorem for periodic cyclic cocycles of a symplectic deformation quantization. The proof of the latter is contained in the sequel to this paper.
We give a proof of a conjecture of P. Schapira and J.-P. Schneiders on the characteristic classes of D-modules.