Local index theorem for projective families
We give a superconnection proof of the cohomological form of Mathai-Melrose-Singer index theorem for the family of twisted Dirac operators under relaxed conditions.
math.DG↗
arXiv subjects
A. Gorokhovsky
Publications and source records attributed to A. Gorokhovsky.
Deformations of gerbes on smooth manifolds
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.
math.QA↗
Deformation quantization of gerbes
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.
math.QA↗
Deformations of Azumaya algebras
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).
math.QA↗