#### 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