Link Invariants and Combinatorial Quantization of Hamiltonian Chern-Simons Theory

E. Buffenoir; Ph. Roche

doi:10.1007/bf02101008

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arXiv · q-alg/9507001

Link Invariants and Combinatorial Quantization of Hamiltonian Chern-Simons Theory

E. Buffenoir·Ph. Roche

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Abstract

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

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BibTeX RIS

E. Buffenoir, Ph. Roche. 1995-07-04. Link Invariants and Combinatorial Quantization of Hamiltonian Chern-Simons Theory. https://doi.org/10.1007/bf02101008

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