Link invariants and combinatorial quantization of hamiltonian Chern Simons theory

1995/07/04 by E. Buffenoir, Ph. Roche · 3 citations
Mathematics · #Advanced Operator Algebra Research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.QA #q-alg

paper · pdf · doi:10.1007/bf02101008

39, latex, 7 figures

arxiv created 1995/07/04 · openalex publication_date 1996/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We define and study the properties of observables associated to any link in Σ× \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=S² these link invariants are pure numbers and are equal to Reshetikhin-Turaev link invariants.

Citations

• Invariants of 3-manifolds via link polynomials and quantum groups
• Representation Theory of Chern Simons Observables

Cited by

• Skein quantization and lattice gauge field theory
• Hamiltonian quantization of Chern Simons theory with SL (2, ) group
• Harmonic Analysis on the Quantum Lorentz Group