q-DEFORMED LATTICE GAUGE THEORY AND 3-MANIFOLD INVARIANTS

Abstract

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 of 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.