TY - JOUR
T1 - A new obstruction of quasialternating links
AU - Qazaqzeh, Khaled
AU - Chbili, Nafaa
N1 - Publisher Copyright:
© 2015, Mathematical Sciences Publishers. All Rights Reserved.
PY - 2015/6/19
Y1 - 2015/6/19
N2 - 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.
AB - 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.
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U2 - 10.2140/agt.2015.15.1847
DO - 10.2140/agt.2015.15.1847
M3 - Article
AN - SCOPUS:84934343286
SN - 1472-2747
VL - 15
SP - 1847
EP - 1862
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
IS - 3
ER -