Geodesic
Studying uniform thickness I: Legendrian simple iterated torus knots
LaFountain, Douglas J1
1Department of Mathematics, University at Buffalo, 244 Mathematics Building, Buffalo, NY 14260, USA
Algebraic and Geometric Topology, Tome 10 (2010) no. 2, pp. 891-916
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We prove that the class of topological knot types that are both Legendrian simple and satisfy the uniform thickness property (UTP) is closed under cabling. An immediate application is that all iterated cabling knot types that begin with negative torus knots are Legendrian simple. We also examine, for arbitrary numbers of iterations, iterated cablings that begin with positive torus knots, and establish the Legendrian simplicity of large classes of these knot types, many of which also satisfy the UTP. In so doing we obtain new necessary conditions for both the failure of the UTP and Legendrian nonsimplicity in the class of iterated torus knots, including specific conditions on knot types.

DOI : 10.2140/agt.2010.10.891
Keywords: Legendrian knots, convex surfaces, uniform thickness property

LaFountain, Douglas J  1

1 Department of Mathematics, University at Buffalo, 244 Mathematics Building, Buffalo, NY 14260, USA 
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LaFountain, Douglas J. Studying uniform thickness I: Legendrian simple iterated torus knots. Algebraic and Geometric Topology, Tome 10 (2010) no. 2, pp. 891-916. doi: 10.2140/agt.2010.10.891

[1] J S Birman, N C Wrinkle, On transversally simple knots, J. Differential Geom. 55 (2000) 325

[2] Y Eliashberg, M Fraser, Topologically trivial Legendrian knots, J. Symplectic Geom. 7 (2009) 77

[3] J B Etnyre, K Honda, Knots and contact geometry. I. Torus knots and the figure eight knot, J. Symplectic Geom. 1 (2001) 63

[4] J B Etnyre, K Honda, Cabling and transverse simplicity, Ann. of Math. $(2)$ 162 (2005) 1305

[5] E Giroux, Convexité en topologie de contact, Comment. Math. Helv. 66 (1991) 637

[6] K Honda, On the classification of tight contact structures. I, Geom. Topol. 4 (2000) 309

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