A new obstruction of quasialternating links

Qazaqzeh, Khaled; Chbili, Nafaa

doi:10.2140/agt.2015.15.1847

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A new obstruction of quasialternating links

Khaled Qazaqzeh and Nafaa Chbili

Algebraic & Geometric Topology 15 (2015) 1847–1862

DOI: 10.2140/agt.2015.15.1847

Abstract

We prove that the degree of the $Q$ –polynomial of any quasialternating link is less than its determinant. Therefore, we obtain a new and simple obstruction criterion for the link to be quasialternating. As an application, we identify some knots of $12$ crossings or less and some links of $9$ crossings or less that are not quasialternating. Our obstruction criterion applies also to show that there are only finitely many Kanenobu knots that are quasialternating. Moreover, we identify an infinite family of Montesinos links that are not quasialternating.

Keywords

quasialternating links, determinant, $Q$–polynomial

Mathematical Subject Classification 2010

Primary: 57M27

References

Publication

Received: 8 July 2014

Revised: 28 September 2014

Accepted: 21 October 2014

Published: 19 June 2015

Authors

Khaled Qazaqzeh
Department of Mathematics Faculty of Science Kuwait University PO Box 5969 Safat-13060, Kuwait State of Kuwait

Nafaa Chbili
Department of Mathematical Sciences College of Science UAE University 15551 Al Ain United Arab Emirates
http://faculty.uaeu.ac.ae/nafaachbili

Volume 15, issue 3 (2015)