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Homotopy field theory in dimension 3 and crossed group-categories

Vladimir Turaev
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Abstract

A 3-dimensional homotopy quantum field theory (HQFT) can be described as a TQFT for surfaces and 3-cobordisms endowed with homotopy classes of maps into a given space. For a group $π$, we introduce a notion of a modular crossed $π$-category and show that such a category gives rise to a 3-dimensional HQFT with target space $K(π,1)$. This includes numerical invariants of 3-dimensional $π$-manifolds and a 2-dimensional homotopy modular functor. We also introduce and discuss a parallel notion of a quasitriangular crossed Hopf $π$-coalgebra.

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Vladimir Turaev. 2000-05-31. Homotopy field theory in dimension 3 and crossed group-categories. https://arxiv.org/abs/math/0005291

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