Coloring link diagrams and Conway-type polynomial of braids

Michael Brandenbursky

doi:10.1016/j.topol.2013.10.017

Coloring link diagrams and Conway-type polynomial of braids

Research output: Contribution to journal › Article › peer-review

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 B_m. 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 language	English
Pages (from-to)	141-158
Number of pages	18
Journal	Topology and its Applications
Volume	161
Issue number	1
DOIs	https://doi.org/10.1016/j.topol.2013.10.017
State	Published - 1 Jan 2014
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2013.10.017

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AB - 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.

KW - Braid groups

KW - Finite type or Vassiliev invariants

KW - HOMFLY-PT and Conway polynomials

KW - Knots

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Coloring link diagrams and Conway-type polynomial of braids

Abstract

Keywords

ASJC Scopus subject areas

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