Parallel Transport on Principal Bundles over Stacks
Differential Geometry
2016-07-20 v1 Mathematical Physics
Category Theory
math.MP
Abstract
In this paper we introduce a notion of parallel transport for principal bundles with connections over differentiable stacks. We show that principal bundles with connections over stacks can be recovered from their parallel transport thereby extending the results of Barrett, Caetano and Picken, and Schreiber and Waldof from manifolds to stacks. In the process of proving our main result we simplify Schreiber and Waldorf's definition of a transport functor for principal bundles with connections over manifolds and provide a more direct proof of the correspondence between principal bundles with connections and transport functors.
Keywords
Cite
@article{arxiv.1509.05000,
title = {Parallel Transport on Principal Bundles over Stacks},
author = {Brian Collier and Eugene Lerman and Seth Wolbert},
journal= {arXiv preprint arXiv:1509.05000},
year = {2016}
}
Comments
33 pages