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AN AXIOMATIC DEFINITION OF HOLONOMY

1994; World Scientific; Volume: 05; Issue: 06 Linguagem: Inglês

10.1142/s0129167x94000425

1793-6519

Ana Paula Caetano, Roger Picken,

Advanced Topics in Algebra

A group of loops [Formula: see text] is associated to every smooth pointed manifold M using a strong homotopy relation. It is shown that the holonomy of a connection on a principal G-bundle may be presented as a group morphism [Formula: see text] and that every such morphism satisfying a natural smoothness condition is the holonomy of some unique connection up to isomorphism.