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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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
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