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Combinatorics of Non-Abelian Gerbes with Connection and Curvature

Romain Attal
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Abstract

We give a functorial definition of $G$-gerbes over a simplicial complex when the local symmetry group $G$ is non-Abelian. These combinatorial gerbes are naturally endowed with a connective structure and a curving. This allows us to define a fibered category equipped with a functorial connection over the space of edge-paths. By computing the curvature of the latter on the faces of an infinitesimal 4-simplex, we recover the cocycle identities satisfied by the curvature of this gerbe. The link with $BF$-theories suggests that gerbes provide a framework adapted to the geometric formulation of strongly coupled gauge theories.

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Romain Attal. 2002-03-27. Combinatorics of Non-Abelian Gerbes with Connection and Curvature. https://arxiv.org/abs/math-ph/0203056

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