Homotopy field theory in dimension 3 and crossed group-categories
Vladimir Turaev
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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