LINK INVARIANTS AND COMBINATORIAL QUANTIZATION OF HAMILTONIAN CHERN-SIMONS THEORY

We define and study the properties of observables associated to any li nk in Sigma xR (where Sigma is a compact surface) using the combinator ial quantization of hamiltonian Chem-Simons theory. These observables are traces of holonomies in a non-commutative Yang-Mills theory where the gauge symmetry is ensured by a quantum group. We show that these o bservables are link invariants taking values in a non-commutative alge bra, the so-called Moduli Algebra. When Sigma=S-2 these link invariant s are pure numbers and are equal to Reshetikhin-Turaev link invariants .