q-deformed lattice gauge theory and 3-manifold invariants

Details q-deformed lattice gauge theory and 3-manifold invariants q-deformed lattice gauge theory and 3-manifold invariants

1992-10-07

arxiv.org/abs/hep-th/9210032v1

Int. J. Mod. Phys. A8 (1993) 3139

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, NBI-HE-92-66

Scientific paper

The notion of $q$-deformed lattice gauge theory is introduced. If the deformation parameter is a root of unity, the weak coupling limit of a 3-$d$ partition function gives a topological invariant for a corresponding 3-manifold. It enables us to define the generalized Turaev-Viro invariant for cell complexes. It is shown that this invariant is determined by an action of a fundamental group on a universal covering of a complex. A connection with invariants of framed links in a manifold is also explored. A model giving a generating function of all simplicial complexes weighted with the invariant is investigated.

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