Central Extensions of Gerbes

TL;DR

This paper introduces the concept of central extensions of gerbes on topological spaces, explores obstruction classes for lifting, and discusses pronilpotent gerbes, with applications to twisted deformation quantization.

Contribution

It defines central extensions of gerbes, analyzes obstruction classes, and discusses pronilpotent gerbes, advancing the theoretical framework for their applications.

Findings

Obstruction classes to lifting objects and isomorphisms are identified.

Central extensions of gerbes are formally introduced and analyzed.

Discussion of pronilpotent gerbes expands the theory.

Abstract

We introduce the notion of central extension of gerbes on a topological space. We then show that there are obstruction classes to lifting objects and isomorphisms in a central extension. We also discuss pronilpotent gerbes. These results are used in a subsequent paper to study twisted deformation quantization on algebraic varieties.