A new proof of the faithfulness of the Temperley–Lieb representation of B 3

Demonstratio mathematica

article

A. H. Piwocki¹ 

[1] Department of Mathematics, Warsaw University

关键词: Kauffman bracket;    Jones polynomial;    Temperley-Lieb representation;    3-braid;    Writhe;   

DOI  :  10.1515/dema-2013-0310

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

We find a way to calculate the term with lowest exponent in the Kauffman bracket polynomial of a closed 3-string braid. This leads us to a new proof of the faithfulness of the Temperley-Lieb representation of the 3-string braid group B 3 . In particular we will prove that for any link with braid index 3 either the coefficient of the lowest degree term or the coefficient of the highest degree term of the Jones polynomial is equal to ±1.

【 授权许可】

CC BY