Geodesic
Cabling and transverse simplicity
John B. Etnyre1 ; Ko Honda2
1 Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104
2 Department of Mathematics, University of Southern California, Los Angeles, CA 90089
Annals of mathematics, Tome 162 (2005) no. 3, pp. 1305-1333.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We study Legendrian knots in a cabled knot type. Specifically, given a topological knot type $\mathcal{K}$, we analyze the Legendrian knots in knot types obtained from $\mathcal{K}$ by cabling, in terms of Legendrian knots in the knot type $\mathcal{K}$. As a corollary of this analysis, we show that the $(2,3)$-cable of the $(2,3)$-torus knot is not transversely simple and moreover classify the transverse knots in this knot type. This is the first classification of transverse knots in a non-transversely-simple knot type. We also classify Legendrian knots in this knot type and exhibit the first example of a Legendrian knot that does not destabilize, yet its Thurston-Bennequin invariant is not maximal among Legendrian representatives in its knot type.
DOI : 10.4007/annals.2005.162.1305

John B. Etnyre 1 ; Ko Honda 2

1 Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104
2 Department of Mathematics, University of Southern California, Los Angeles, CA 90089 
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John B. Etnyre; Ko Honda. Cabling and transverse simplicity. Annals of mathematics, Tome 162 (2005) no. 3, pp. 1305-1333. doi : 10.4007/annals.2005.162.1305. http://geodesic.mathdoc.fr/articles/10.4007/annals.2005.162.1305/

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