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QUASI-ALTERNATING MONTESINOS LINKS

TAMARA WIDMER

Institute of Mathematics, University of Zurich, Switzerland

https://doi.org/10.1142/S0218216509007518Cited by:11 (Source: Crossref)

Abstract

The aim of this article is to detect new classes of quasi-alternating links. Quasi-alternating links are a natural generalization of alternating links. Their knot Floer and Khovanov homology are particularly easy to compute. Since knot Floer homology detects the genus of a knot as well as whether a knot is fibered, characterization of quasi-alternating links becomes an interesting open problem. We show that there exist classes of non-alternating Montesinos links, which are quasi-alternating.

Keywords:

AMSC: 57M25

References

T. Abe and K. Kishimoto, The dealternating number and the alternation number of a closed 3-braid, preprint, arXiv, math.GT, Jan 2008, http://arxiv.org/. In the December 2008 version of the paper Section 6 is rewritten , arXiv:0808.0573v2 . Google Scholar
C. C. Adamset al., Topol. Appl. 46(2), 151 (1992). Web of Science, Google Scholar
J. A. Baldwin, J. Topol. 1(4), 963 (2008), DOI: 10.1112/jtopol/jtn029. Web of Science, Google Scholar
C. Bankwitz and H. G. Schumann, Abh. Math. Sem. Univ. Hamburg 10, 263 (1934), DOI: 10.1007/BF02940679. 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), DOI: 10.1090/S0002-9939-09-09876-1. Web of Science, Google Scholar
O. T. Dasbach, D. Futer, E. Kalfagianni, X. Lin and N. W. Stoltzfus, Alternating sum formulae for the determinant and other link invariants, preprint, arXiv, math.GT, Nov 2006, http://aexiv.org/abs/ , math.GT/0611025v2 . Google Scholar
O. T. Dasbachet al., J. Combin. Theory Ser. B 98(2), 384 (2008), DOI: 10.1016/j.jctb.2007.08.003. Web of Science, Google Scholar
C. Ernst and D. W. Sumners, Math. Proc. Cambridge Phil. Soc. 108, 489 (1990), DOI: 10.1017/S0305004100069383. Web of Science, Google Scholar
J. Greene, Homologically thin, non-quasi-alternating links, preprint, arXiv, math.GT, Jan 2009, http://arxiv.org/abs/ , arXiv:0906.2222v1 . Google Scholar
S. Jablan and R. Sazdanović, Quasi-alternating links and odd homology: Computations and conjectures, preprint, arXiv, math.GT, Jan 2008, http://arxiv.org/abs/ , arXiv:0901.0075v1 . Google Scholar
L. H. Kauffman and P. Lopes, Graded forests and rational knots, preprint, arXiv, math.GT, Oct 2007, http://arxiv.org/abs/ , arXiv:0710.3765v1 . Google Scholar
W. B. R. Lickorish , An Introduction to Knot Theory , Graduate Texts in Mathematics 175 ( Springer-Verlag , New York , 1997 ) . Google Scholar
W. B. R. Lickorish and M. B. Thistlethwaite, Comment. Math. Helvetici 63, 527 (1998), DOI: 10.1007/BF02566777. Web of Science, Google Scholar
A. Lowrance, Algebr. Geom. Topol. 8(2), 1141 (2008), DOI: 10.2140/agt.2008.8.1141. Web of Science, Google Scholar
C. Manolescu, Math. Res. Lett. 14(5), 839 (2007). Web of Science, Google Scholar
C. Manolescu and P. Ozsvath, On the Khovanov and knot Floer homologies of quasi-alternating links, Proceedings of the 14th Gökova Geometry-Topology Conference (2007) pp. 60–81. Google Scholar
P. Ozsvath and Z. Szabo, Adv. Math. 194(1), 1 (2005), DOI: 10.1016/j.aim.2004.05.008. Web of Science, Google Scholar