The fundamental Gray 3-groupoid of a smooth manifold and local 3-dimensional holonomy based on a 2-crossed module

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Abstract

We define the thin fundamental Gray 3-groupoid S-3(M) of a smooth manifold M and define (by using differential geometric data) 3-dimensional holonomies, to be smooth strict Gray 3-groupoid maps S-3(M) -> C(H), where H is a 2-crossed module of Lie groups and C(H) is the Gray 3-groupoid naturally constructed from H. As an application, we define Wilson 3-sphere observables. (C) 2010 Elsevier B.V. All rights reserved.
Original languageUnknown
Pages (from-to)179-206
JournalDifferential Geometry And Its Applications
Volume29
Issue number2
DOIs
Publication statusPublished - 1 Jan 2011

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