Parallel transport on principal bundles over stacks

Brian Collier, Eugene Lerman, Seth Wolbert

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageEnglish (US)
Pages (from-to)187-213
Number of pages27
JournalJournal of Geometry and Physics
Volume107
DOIs
StatePublished - Sep 1 2016

Keywords

  • Holonomy
  • Lie groupoids
  • Parallel transport
  • Principal bundles
  • Stacks
  • Wilson lines

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

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