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

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

2002-10-21

arxiv.org/abs/math/0210322v1

Mathematics

Differential Geometry

10 pages, Latex2E

Scientific paper

Our 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-$\dot{\rm I}$\c{c}en-Mucuk.

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