A new two-variable generalization of the Jones polynomial-Reference-Cited by-同舟云学术

A new two-variable generalization of the Jones polynomial

Published:2019-10 Issue:11 Volume:28 Page:1940005
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Goundaroulis Dimos¹²,Lambropoulou Sofia³

Affiliation:

1. Center for Integrative Genomics, University of Lausanne, CH-1015 Lausanne, Switzerland

2. Swiss Institute of Bioinformatics, CH-1015 Lausanne, Switzerland

3. Department of Mathematics, National Technical University of Athens, Zografou Campus, GR–157 80 Athens, Greece

Abstract

We present a new 2-variable generalization of the Jones polynomial that can be defined through the skein relation of the Jones polynomial. The well-definedness of this invariant is proved both algebraically and diagrammatically as well as via a closed combinatorial formula. This new invariant is able to distinguish more pairs of nonisotopic links than the original Jones polynomial, such as the Thistlethwaite link from the unlink with two components.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216519400054

Reference28 articles.

1. Markov Trace on the Algebra of Braids and Ties

2. Tied links

3. THE YOKONUMA–HECKE ALGEBRAS AND THE HOMFLYPT POLYNOMIAL

4. On the link invariants from the Yokonuma–Hecke algebras

5. The HOMFLY-PT polynomials of sublinks and the Yokonuma–Hecke algebras

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