A formal moment map on $\textrm{Diff}_0(M)$

TL;DR

This paper develops a deformation of the Donaldson moment map within the context of deformation quantization, applied to the connected component of the diffeomorphism group of a symplectic manifold with an additional symplectic structure.

Contribution

It introduces a novel deformation of the Donaldson moment map in the setting of deformation quantization for symplectic manifolds.

Findings

Deformation of the Donaldson moment map constructed

Application to symplectic manifolds with multiple structures

Advancement in understanding symplectic diffeomorphism groups

Abstract

In the framework of deformation quantization, we obtain a deformation of Donaldson moment map on $\textrm{Diff}_0(M)$, the connected component of the group of diffeomorphisms of a symplectic manifold $(M,\omega)$ admitting another symplectic structure $\chi$.