Link invariants and combinatorial quantization of Hamiltonian Chern Simons theory

DOI10.1007/BF02101008zbMATH Open0857.58046arXivq-alg/9507001MaRDI QIDQ1925002

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Publication date: 10 March 1997

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Abstract: We define and study the properties of observables associated to any link in $$ (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.

Full work available at URL: https://arxiv.org/abs/q-alg/9507001

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