On 2-Holonomy
Algebraic Topology
2021-07-01 v1 Mathematical Physics
K-Theory and Homology
math.MP
Rings and Algebras
Abstract
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.
Cite
@article{arxiv.1202.2292,
title = {On 2-Holonomy},
author = {Hossein Abbaspour and Friedrich Wagemann},
journal= {arXiv preprint arXiv:1202.2292},
year = {2021}
}