4,321 research outputs found
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.Comment: Revised versio
A variant of the Mukai pairing via deformation quantization
We give a new method to prove a formula computing a variant of Caldararu's
Mukai pairing \cite{Cal1}. Our method is based on some important results in the
area of deformation quantization. In particular, part of the work of Kashiwara
and Schapira in \cite{KS} as well as an algebraic index theorem of Bressler,
Nest and Tsygan in \cite{BNT},\cite{BNT1} and \cite{BNT2} are used. It is hoped
that our method is useful for generalization to settings involving certain
singular varieties.Comment: 8 pages. Comments and suggestions welcom
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