Link Invariants and Combinatorial Quantization of Hamiltonian Chern-Simons Theory

Abstract

We define and study the properties of observables associated to any link in $\Sigma \times \mathbf{R}$ (where $\Sigma$ 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 $\Sigma =S^2$ these link invariants are pure numbers and are equal to Reshetikhin-Turaev link invariants.

39, latex, 7 figures

References in corpus (5)

• Combinatorial quantization of the Hamiltonian Chern-Simons theory I
• Two dimensional lattice gauge theory based on a quantum group
• Intersections forms and the geometry of lattice Chern-Simons theory
• Chern-Simons Perturbation Theory
• Representation Theory of Chern Simons Observables

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