Coloring link diagrams and Conway-type polynomial of braids

2013/02/28 by Michael Brandenbursky
Mathematics · #Advanced Combinatorial Mathematics #Alexander polynomial #Braid #Combinatorics #Discrete mathematics #Geometric and Algebraic Topology #HOMFLY polynomial #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Knot theory #Link (geometry) #Mathematical analysis #Mathematics #Matrix polynomial #Polynomial #Pure mathematics #Square-free polynomial #Type (biology) #math.GT

paper · pdf · doi:10.1016/j.topol.2013.10.017

This is a revised version. To appear in Topology and its Applications

arxiv created 2013/10/08 · arxiv updated 2013/10/09 · openalex publication_date 2013/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper we define and present a simple combinatorial formula for a 3-variable Laurent polynomial invariant of conjugacy classes in Artin braid group B_m. We show that this Laurent polynomial satisfies the Conway skein relation and its coefficients are Vassiliev invariants of braids.

Citations

• On the Vassiliev knot invariants
• Finite-type invariants of classical and virtual knots
• An Introduction to Knot Theory
• Link invariants via counting surfaces