Differential Geometry of Gerbes and Differential Forms

TL;DR

This paper explores the differential geometry of non-abelian gerbes, refining cocycle equations and demonstrating that diagrammatic proofs can be replaced by differential form computations.

Contribution

It provides a more direct derivation of cocycle equations and introduces a more restrictive definition of coboundary relations for non-abelian gerbes.

Findings

Refined cocycle equations for non-abelian gerbes

A more restrictive coboundary relation definition

Differential form computations replace diagrammatic proofs

Abstract

We discuss certain aspects of the combinatorial approach to the differential geometry of non-abelian gerbes, due to W. Messing and the author (arXiv:math.AG/0106083), and give a more direct derivation of the associated cocycle equations. This leads us to a more restrictive definition of the corresponding coboundary relations. We also show that the diagrammatic proofs of certain local curving and curvature equations may be replaced by computations with differential forms.