Parallel transport on principal bundles over stacks

JOURNAL OF GEOMETRY AND PHYSICS

卷:107

Article

Collier, Brian¹  Lerman, Eugene¹  Wolbert, Seth¹ 

[1] Univ Illinois, Dept Math, 1409 W Green St, Urbana, IL 61801 USA

关键词: Parallel transport;    Principal bundles;    Stacks;    Wilson lines;    Holonomy;    Lie groupoids;   

DOI  :  10.1016/j.geomphys.2016.05.010

来源: Elsevier

【 摘 要 】

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 Waldorf from manifolds to stacks. In the process of proving our main result we simplify Schreiber and Waldorfs original 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. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free