dorsal/arxiv
View SchemaLink Invariants and Combinatorial Quantization of Hamiltonian Chern-Simons Theory
| Authors | E. Buffenoir, Ph. Roche |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9507001 |
| URL | https://arxiv.org/abs/q-alg/9507001 |
| DOI | 10.1007/BF02101008 |
Abstract
We define and study the properties of observables associated to any link in $\Sigma\times {\bf R}$ (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.
{
"annotation_id": "26e36b3f-6aa7-4f14-8154-ca1841086e22",
"date_created": "2026-03-02T18:01:25.152000Z",
"date_modified": "2026-03-02T18:01:25.152000Z",
"file_hash": "938f55bcff13e1793deec0ebef0c8008fcee804bcc24d927d885241fa2e342f0",
"private": false,
"record": {
"abstract": "We define and study the properties of observables associated to any link in\n$\\Sigma\\times {\\bf R}$ (where $\\Sigma$ is a compact surface) using the\ncombinatorial quantization of hamiltonian Chern-Simons theory. These\nobservables are traces of holonomies in a non commutative Yang-Mills theory\nwhere the gauge symmetry is ensured by a quantum group. We show that these\nobservables are link invariants taking values in a non commutative algebra, the\nso called Moduli Algebra. When $\\Sigma=S^2$ these link invariants are pure\nnumbers and are equal to Reshetikhin-Turaev link invariants.",
"arxiv_id": "q-alg/9507001",
"authors": [
"E. Buffenoir",
"Ph. Roche"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1007/BF02101008",
"title": "Link Invariants and Combinatorial Quantization of Hamiltonian Chern-Simons Theory",
"url": "https://arxiv.org/abs/q-alg/9507001"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "87589f86-d90e-443b-be69-143e373f11e9",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}