Coloring link diagrams and Conway-type polynomial of braids

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Abstract

In this paper we define and present a simple combinatorial formula for a 3-variable Laurent polynomial invariant I(a, z, t) of conjugacy classes in Artin braid group Bm. We show that the Laurent polynomial I(a, z, t) satisfies the Conway skein relation and the coefficients of the 1-variable polynomial t-kI(a, z, t)|a=1,t=0 are Vassiliev invariants of braids.

Original languageEnglish
Pages (from-to)141-158
Number of pages18
JournalTopology and its Applications
Volume161
Issue number1
DOIs
StatePublished - 1 Jan 2014
Externally publishedYes

Keywords

  • Braid groups
  • Finite type or Vassiliev invariants
  • HOMFLY-PT and Conway polynomials
  • Knots

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