Parallel transport on principal bundles over stacks
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- 作者：Brian Collier ; Eugene Lerman ; lerman@math.uiuc.edu" class="auth_mail" title="E-mail the corresponding author ; Seth Wolbert
- 关键词：Parallel transport ; Principal bundles ; Stacks ; Wilson lines ; Holonomy ; Lie groupoids
- 刊名：Journal of Geometry and Physics
- 出版年：2016
- 出版时间：September 2016
- 年：2016
- 卷：107
- 期：Complete
- 页码：187-213
- 全文大小：578 K
文摘
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 Waldorf’s 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.