Connections, local subgroupoids,and a holonomy Lie groupoid of a line bundle gerbe

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dc.creatorBrown, Ronald
dc.creatorGlazebrook, James F.
dc.date2002-10-21
dc.date.accessioned2026-07-07T04:52:11Z
dc.date.available2026-07-07T04:52:11Z
dc.descriptionOur main aim is to associate a holonomy Lie groupoid to the connective structure of an abelian gerbe. The construction has analogies with a procedure for the holonomy Lie groupoid of a foliation, in using a locally Lie groupoid and a globalisation procedure. We show that path connections and 2-holonomy on line bundles may be formulated using the notion of a connection pair on a double category, due to Brown-Spencer, but now formulated in terms of double groupoids using the thin fundamental groupoids introduced by Caetano-Mackaay-Picken. To obtain a locally Lie groupoid to which globalisation applies, we use methods of local subgroupoids as developed by Brown-$\dot{\rm I}$çen-Mucuk.
dc.description10 pages, Latex2E
dc.identifierhttps://arxiv.org/abs/math/0210322
dc.identifierhttp://arxiv.org/abs/math/0210322
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65374
dc.subjectDifferential Geometry
dc.subjectCategory Theory
dc.subject18F20, 18F05, 22E99, 58H05
dc.titleConnections, local subgroupoids,and a holonomy Lie groupoid of a line bundle gerbe
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