Formality theorem for gerbes

TL;DR

This paper extends Kontsevich's formality theorem from deformations of the structure sheaf to deformations of gerbes on smooth and complex manifolds, broadening the scope of deformation theory in geometry.

Contribution

It introduces a formality theorem for gerbes, generalizing existing results from sheaves to higher categorical structures on manifolds.

Findings

Established a formality theorem for gerbes on smooth manifolds

Extended deformation theory to include gerbes

Bridged the gap between sheaf and gerbe deformations

Abstract

We extend the formality theorem of Maxim Kontsevich from deformations of the structure sheaf on a manifold to deformations of gerbes on smooth and complex manifolds.