dorsal/arxiv
View SchemaOn Vassiliev Invariants for Links in Handlebodies
| Authors | V. V. Vershinin |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9709017 |
| URL | https://arxiv.org/abs/q-alg/9709017 |
| Journal | J. Knot Theory Ramifications 7 (1998), no. 5, 701-712 |
Abstract
The notion of Vassiliev algebra in case of hanlebodies is developed. The analogues of the results of John Baez for links in handlebodies are proved. That means that there exists a one-to-one correspondence between the special class of finite type invariants of links in hanlebodies and the homogeneous Markov traces on Vassiliev algebras. This approach uses the singular braid monoid and braid group in a handlebody and the generalizations of the theorem of J. Alexander and the theorem of A. A. Markov for singular links and braids and the relative version of Markov's theorem.
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"abstract": "The notion of Vassiliev algebra in case of hanlebodies is developed. The\nanalogues of the results of John Baez for links in handlebodies are proved.\nThat means that there exists a one-to-one correspondence between the special\nclass of finite type invariants of links in hanlebodies and the homogeneous\nMarkov traces on Vassiliev algebras. This approach uses the singular braid\nmonoid and braid group in a handlebody and the generalizations of the theorem\nof J. Alexander and the theorem of A. A. Markov for singular links and braids\nand the relative version of Markov\u0027s theorem.",
"arxiv_id": "q-alg/9709017",
"authors": [
"V. V. Vershinin"
],
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"q-alg",
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],
"journal_ref": "J. Knot Theory Ramifications 7 (1998), no. 5, 701-712",
"title": "On Vassiliev Invariants for Links in Handlebodies",
"url": "https://arxiv.org/abs/q-alg/9709017"
},
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