A new obstruction of quasialternating links

Qazaqzeh, Khaled¹ ; Chbili, Nafaa²

¹Department of Mathematics, Faculty of Science, Kuwait University, PO Box 5969, Safat-13060, Kuwait, State of Kuwait
²Department of Mathematical Sciences, College of Science UAE University, 15551 Al Ain, United Arab Emirates

Algebraic and Geometric Topology, Tome 15 (2015) no. 3, pp. 1847-1862

Résumé

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.

Détail

DOI : 10.2140/agt.2015.15.1847

Classification : 57M27
Keywords: quasialternating links, determinant, $Q$–polynomial

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