On the Jones polynomial of quasi-alternating links

Nafaa Chbili, Khaled Qazaqzeh

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We prove that twisting any quasi-alternating link L with no gaps in its Jones polynomial VL(t) at the crossing where it is quasi-alternating produces a link L with no gaps in its Jones polynomial VL (t). This leads us to conjecture that the Jones polynomial of any prime quasi-alternating link, other than (2,n)-torus links, has no gaps. This would give a new property of quasi-alternating links and a simple obstruction criterion for a link to be quasi-alternating. We prove that the conjecture holds for quasi-alternating Montesinos links as well as quasi-alternating links with braid index 3.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalTopology and its Applications
Volume264
DOIs
Publication statusPublished - Sep 1 2019

Keywords

  • 3-braids
  • Jones polynomial
  • Montesinos links
  • Quasi-alternating links

ASJC Scopus subject areas

  • Geometry and Topology

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