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Maximal Thurston-Bennequin number of $ +$adequate links

Author(s): Tamás Kálmán
Journal: Proc. Amer. Math. Soc. 136 (2008), 2969-2977.
MSC (2000): Primary 57M25; Secondary 53D12
Posted: April 7, 2008
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Abstract: The class of $ +$adequate links contains both alternating and positive links. Generalizing results of Tanaka (for the positive case) and Ng (for the alternating case), we construct fronts of an arbitrary $ +$adequate link $ A$ so that the diagram has a ruling; therefore its Thurston-Bennequin number is maximal among Legendrian representatives of $ A$. We derive consequences for the Kauffman polynomial and Khovanov homology of $ +$adequate links.


References:

1.
P. Cromwell: Knots and Links, Cambridge University Press, 2004. MR 2107964 (2005k:57011)

2.
J. Etnyre: Legendrian and transversal knots, in Handbook of Knot Theory, Elsevier B. V., Amsterdam, 2005, 105-185. MR 2179261 (2006j:57050)

3.
J. Etnyre and K. Honda: Knots and contact geometry I: torus knots and the figure eight knot, J. Symplectic Geom. 1 (2001), no. 1, 63-120. MR 1959579 (2004d:57032)

4.
D. Fuchs: Chekanov-Eliashberg invariants of Legendrian knots: existence of augmentations, J. Geom. Phys. 47 (2003), no. 1, 43-65. MR 1985483 (2004h:57007)

5.
L. H. Kauffman: Knots and Physics, Series on Knots and Everything, vol. 1, World Scientific, New Jersey, 1991. MR 1141156 (93b:57010)

6.
T. Kálmán: Contact homology and one parameter families of Legendrian knots, Geom. Topol. 9 (2005), 2013-2078. MR 2209366 (2007c:53126)

7.
W. B. R. Lickorish and M. B. Thistlethwaite: Some links with non-trivial polynomials and their crossing numbers, Comment. Math. Helv. 63 (1988), no. 4, 527-539. MR 966948 (90a:57010)

8.
L. Ng: Maximal Thurston-Bennequin number of two-bridge links, Algebr. Geom. Topol. 1 (2001), 427-434. MR 1852765 (2002e:57020)

9.
L. Ng: A Legendrian Thurston-Bennequin bound from Khovanov homology, Algebr. Geom. Topol. 5 (2005), 1637-1653. MR 2186113 (2007g:57027)

10.
L. Rudolph: A congruence between link polynomials, Math. Proc. Camb. Phil. Soc. 107 (1990), 319-327. MR 1027784 (90k:57010)

11.
D. Rutherford: Thurston-Bennequin number, Kauffman polynomial, and ruling invariants of a Legendrian link: the Fuchs conjecture and beyond, Int. Math. Res. Not. 2006, Art. ID 78591. MR 2219227 (2007a:57020)

12.
T. Tanaka: Maximal Bennequin numbers and Kauffman polynomials of positive links, Proc. Amer. Math. Soc. 127 (1999), 3427-3432. MR 1616601 (2000b:57014)

13.
T. Tanaka: Maximal Thurston-Bennequin numbers of alternating links, Topology Appl. 153 (2006), 2476-2483. MR 2243727 (2007f:57026)

14.
M. B. Thistlethwaite: On the Kauffman polynomial of an adequate link, Invent. Math. 93 (1988), 285-296. MR 948102 (89g:57009)

15.
Y. Yokota: Polynomial invariants of positive links, Topology 31 (1992), no. 4, 805-811. MR 1191382 (93k:57028)

16.
Y. Yokota: The Kauffman polynomial of alternating links, Topology Appl. 65 (1995), 229-236. MR 1357866 (96m:57020)


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Additional Information:

Tamás Kálmán
Affiliation: Graduate School of Mathematics, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan
Email: kalman@ms.u-tokyo.ac.jp

DOI: 10.1090/S0002-9939-08-09478-1
PII: S 0002-9939(08)09478-1
Received by editor(s): November 9, 2006
Posted: April 7, 2008
Communicated by: Daniel Ruberman
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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