期刊
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
卷 22, 期 3, 页码 -出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218216513500119
关键词
Braid groups; knot polynomials; finite type invariants; Gauss diagram formulas
类别
资金
- Oberwolfach Leibniz fellowship
A Gauss diagram is a simple, combinatorial way to present a link. It is known that any Vassiliev invariant may be obtained from a Gauss diagram formula that involves counting subdiagrams of certain combinatorial types. In this paper we present simple formulas for an infinite family of invariants in terms of counting surfaces of a certain genus and number of boundary components in a Gauss diagram associated with a closed braid. We then identify the resulting invariants with partial derivatives of the HOMFLYPT polynomial.
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