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Topological invariant of 4-manifolds based on a 3-group
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We study a generalization of a 4-dimensional BF-theory in the context of higher gauge theory. We construct a triangulation independent topological state sum Z, based on the classical 3BF action for a general 3-group and a 4-dimensional spacetime manifold. This state sum coincides with Porter's TQFT for d=4 and n=3. In order to verify that the constructed state sum is a topological invariant of the underlying 4-dimensional manifold, its behavior under Pachner moves is analyzed, and it is obtained that the state sum Z remains the same. This paper is a generalization of the work done by Girelli, Pfeiffer, and Popescu for the case of state sum based on the classical 2BF action with the underlying 2-group structure.
Forward citations
Cited by 2 Pith papers
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A 3BF model of quantum gravity coupled to Standard Model matter
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 3BF theory as a TQFT
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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