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Quasi-alternating links and Q-polynomials

Masakazu Teragaito

Department of Mathematics Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-Hiroshima, 739-8524, Japan

https://doi.org/10.1142/S0218216514500680Cited by:11 (Source: Crossref)

Abstract

Qazaqzeh and Chbili showed that for any quasi-alternating link, the degree of the Q-polynomial is less than its determinant. We give a refinement of their evaluation.

Keywords:

AMSC: 57M25, 57M27

References

C. Bankwitz, Math. Ann. 103(1), 145 (1930). Crossref, Google Scholar
R. D. Brandt, W. B. R. Lickorish and K. C. Millett, Invent. Math. 84(3), 563 (1986). Crossref, Web of Science, Google Scholar
J. C. Cha and C. Livingston, KnotInfo: Table of knot invariants, http://www.indiana.edu/knotinfo . Google Scholar
A. Champanerkar and I. Kofman, Proc. Amer. Math. Soc. 137(7), 2451 (2009). Crossref, Web of Science, Google Scholar
R. H. Crowell , Illinois J. Math. 3 , 101 ( 1959 ) . Crossref, Google Scholar
J. Greene, Math. Res. Lett. 17(1), 39 (2010). Crossref, Web of Science, Google Scholar
J. Greene and L. Watson, Bull. Lond. Math. Soc. 45(5), 962 (2013). Crossref, Web of Science, Google Scholar
C. F. Ho, Abstracts Amer. Math. Soc. 6(4), 300 (1985). Web of Science, Google Scholar
C. Hodgson and J. H. Rubinstein, Knot Theory and Manifolds, Lecture Notes in Mathematics 1144 (Springer, Berlin, 1985) pp. 60–96. Crossref, Google Scholar
S. Jablan, Tables of quasi-alternating knots with at most 12 crossings, preprint (2014) , arXiv:1404.4965 . Google Scholar
P. Kronheimeret al., Ann. of Math. (2) 165(2), 457 (2007). Crossref, Web of Science, Google Scholar
C. Manolescu and P. Ozsváth, On the Khovanov and knot Floer homologies of quasi-alternating links, Proc. 14th Gokova Geometry-Topology Conf. (International Press, Somerville, MA, USA, 2007) pp. 60–81. Google Scholar
L. Moser , Pacific J. Math. 38 , 737 ( 1971 ) . Crossref, Web of Science, Google Scholar
P. Ozsváth and Z. Szabó , Geom. Topol. 8 , 311 ( 2004 ) . Crossref, Web of Science, Google Scholar
P. Ozsváth and Z. Szabó, Adv. Math. 194(1), 1 (2005). Crossref, Web of Science, Google Scholar
K. Qazaqzeh and N. Chbili, A new obstruction of quasi-alternating links, preprint (2014) , arXiv:1406.0279 . Google Scholar
K. Qazaqzeh, B. Qublan and A. Jaradat, J. Knot Theory Ramifications 22(6), 13 (2013). Link, Web of Science, Google Scholar
M. Sakuma, Algebraic and Topological Theories (Kinokuniya, Tokyo, 1986) pp. 176–196. Google Scholar
M. Tange, Math. Proc. Cambridge Philos. Soc. 146(1), 119 (2009). Crossref, Web of Science, Google Scholar
T. Widmer, J. Knot Theory Ramifications 18(10), 1459 (2009). Link, Web of Science, Google Scholar