English

A new two-variable generalization of the Jones polynomial

Geometric Topology 2018-11-09 v4

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 new generalization is proved both algebraically and diagrammatically as well as via a closed combinatorial formula. This new invariant is able to distinguish more pairs of non-isotopic links than the original Jones polynomial such as the Thistlethwaite link from the unlink with two components.

Keywords

Cite

@article{arxiv.1608.01812,
  title  = {A new two-variable generalization of the Jones polynomial},
  author = {Dimos Goundaroulis and Sofia Lambropoulou},
  journal= {arXiv preprint arXiv:1608.01812},
  year   = {2018}
}

Comments

18 pages, 7 figures

R2 v1 2026-06-22T15:13:07.568Z