Homotopy field theory in dimension 3 and crossed group-categories

Details Homotopy field theory in dimension 3 and crossed group-categories Homotopy field theory in dimension 3 and crossed group-categories

2000-05-31

arxiv.org/abs/math/0005291v1

Mathematics

Geometric Topology

76 pages, no figures

Scientific paper

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 $\pi$, we introduce a notion of a modular crossed $\pi$-category and show that such a category gives rise to a 3-dimensional HQFT with target space $K(\pi,1)$. This includes numerical invariants of 3-dimensional $\pi$-manifolds and a 2-dimensional homotopy modular functor. We also introduce and discuss a parallel notion of a quasitriangular crossed Hopf $\pi$-coalgebra.

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