Invariants of closed braids via counting surfaces

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2 Scopus citations


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 HOMFLY-PT polynomial.

Original languageEnglish
Article number13500119
JournalJournal of Knot Theory and its Ramifications
Issue number3
StatePublished - 1 Mar 2013
Externally publishedYes


  • Braid groups
  • Gauss diagram formulas
  • finite type invariants
  • knot polynomials

ASJC Scopus subject areas

  • Algebra and Number Theory


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