#### Volume 15, issue 3 (2015)

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A new obstruction of quasialternating links

### Khaled Qazaqzeh and Nafaa Chbili

Algebraic & Geometric Topology 15 (2015) 1847–1862
##### 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
Primary: 57M27
##### 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