dorsal/arxiv
View SchemaThe Fundamental Theorem of Vassiliev Invariants
| Authors | Dror Bar-Natan, Alexander Stoimenow |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9702009 |
| URL | https://arxiv.org/abs/q-alg/9702009 |
Abstract
The "fundamental theorem of Vassiliev invariants" says that every weight system can be integrated to a knot invariant. We discuss four different approaches to the proof of this theorem: a topological/combinatorial approach following M. Hutchings, a geometrical approach following Kontsevich, an algebraic approach following Drinfel'd's theory of associators, and a physical approach coming from the Chern-Simons quantum field theory. Each of these approaches is unsatisfactory in one way or another, and hence we argue that we still don't really understand the fundamental theorem of Vassiliev invariants.
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"abstract": "The \"fundamental theorem of Vassiliev invariants\" says that every weight\nsystem can be integrated to a knot invariant. We discuss four different\napproaches to the proof of this theorem: a topological/combinatorial approach\nfollowing M. Hutchings, a geometrical approach following Kontsevich, an\nalgebraic approach following Drinfel\u0027d\u0027s theory of associators, and a physical\napproach coming from the Chern-Simons quantum field theory. Each of these\napproaches is unsatisfactory in one way or another, and hence we argue that we\nstill don\u0027t really understand the fundamental theorem of Vassiliev invariants.",
"arxiv_id": "q-alg/9702009",
"authors": [
"Dror Bar-Natan",
"Alexander Stoimenow"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "The Fundamental Theorem of Vassiliev Invariants",
"url": "https://arxiv.org/abs/q-alg/9702009"
},
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