A QUANTUM GROUP VERSION OF QUANTUM GAUGE-THEORIES IN 2 DIMENSIONS

For the special case of the quantum group SL(q)(2, C) (q = exp(pii/r), r greater-than-or-equal-to 3) we present an alternative approach to quantum gauge theories in two dimensions. We exhibit the similarities to Witten's combinatorial approach which is based on the ideas of Migdal. The main ingredient is the Turaev-Viro combinatorial construction of topological invariants of closed, compact 3-manifolds and its extension to arbitrary compact 3-manifolds as given by the authors in collaboration with W Muller.