  For the special case of the quantum group $SL_q (2,{\bf C})\ (q= \exp \pi
i/r,\ r\ge 3)$ 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 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. Mueller.
