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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

classification math.CThep-thmath.DG
keywords graygroupoiddefinesmoothcrosseddimensionalfundamentalmanifold
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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 $S_3(M) \to C(H)$, 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 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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    A 3BF higher-gauge model of quantum gravity with the full Standard Model is discretized on a piecewise-flat manifold, yielding a concrete path integral.

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    The five-dimensional topological axion electrodynamics is shown to possess a 3-crossed module structure through modified Stueckelberg couplings required for background gauge invariance.

  3. Generalized forms of types N = 1, 2 and higher gauge theory

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    Strict 2- and 3-gauge theory is re-expressed in a single generalized-form formalism in which higher connections, curvatures, Bianchi identities, and gauge transformations match ordinary gauge-theory form, yielding uni...

  4. The 3BF theory as a TQFT

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    A boundary state sum for the 3BF theory is constructed and proved to satisfy Atiyah's axioms, giving a TQFT functor for finite 3-groups on triangulable 4-manifolds.

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