On Khovanov Homology of Quasi-Alternating Links

Khaled Qazaqzeh, Nafaa Chbili

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that the length of any gap in the differential grading of the Khovanov homology of any quasi-alternating link is one. As a consequence, we obtain that the length of any gap in the Jones polynomial of any such link is one. This establishes a weaker version of Conjecture 2.3 in (Topol Appl 264:1–11, 2019). Moreover, we obtain a lower bound for the determinant of any such link in terms of the breadth of its Jones polynomial. This establishes a weaker version of Conjecture 3.8 in (Algebr Geom Topol 15:1847–1862, 2015). The main tool in obtaining this result is establishing the Knight Move Conjecture [(Algebr Geom Topol 2:337-370, 2002), Conjecture 1] for the class of quasi-alternating links.

Original languageEnglish
Article number104
JournalMediterranean Journal of Mathematics
Volume19
Issue number3
DOIs
Publication statusPublished - Jun 2022

Keywords

  • Breadth
  • Jones polynomial
  • Khovanov homology
  • Quasi-alternating

ASJC Scopus subject areas

  • General Mathematics

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