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

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arxiv 0907.2566 v3 pith:5QMXJDEB submitted 2009-07-15 math.CT hep-thmath.DG

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

classification math.CT hep-thmath.DG
keywords graygroupoiddefinesmoothcrosseddimensionalfundamentalmanifold
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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 $S_3(M) \to C(H)$, 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.

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Cited by 3 Pith papers

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