  We describe an approach to the quantisation of (2+1)-dimensional gravity with
topology R x T^2 and negative cosmological constant, which uses two quantum
holonomy matrices satisfying a q-commutation relation. Solutions of diagonal
and upper-triangular form are constructed, which in the latter case exhibit
additional, non-trivial internal relations for each holonomy matrix.
Representations are constructed and a group of transformations - a
quasi-modular group - which preserves this structure, is presented.
