On 2-Holonomy

Hossein Abbaspour (1) , Friedrich Wagemann (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

We construct a cycle in higher Hochschild homology associated to the 2-dimensional torus which represents 2-holonomy of a non-abelian gerbe in the same way the ordinary holonomy of a principal G-bundle gives rise to a cycle in ordinary Hochschild homology. This is done using the connection 1-form of Baez-Schreiber. A crucial ingredient in our work is the possibility to arrange that in the structure crossed module mu: g -> h of the principal 2-bundle, the Lie algebra h is abelian, up to equivalence of crossed modules.

Domaines: Topologie algébrique [math.AT]; K-théorie et homologie [math.KT]; Anneaux et algèbres [math.RA]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Hossein Abbaspour, Friedrich Wagemann. On 2-Holonomy. 2012. ⟨hal-01057775⟩