Link invariants and combinatorial quantization of hamiltonian Chern Simons theory

We define and study the properties of observables associated to any link in ×R (where is a compact surface) using the combinatorial quantization of hamiltonian Chern-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 observables are link invariants taking values in a non-commutative algebra, the so-called Moduli Algebra. When =S² these link invariants are pure numbers and are equal to Reshetikhin-Turaev link invariants.Laboratoire Propre du CNRS UPR 14.