Cabling and transverse simplicity

• Autores: John B. Etnyre, Ko Honda
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 162, Nº 3, 2005, págs. 1303-1331
• Idioma: inglés
• DOI: 10.4007/annals.2005.162.1305
• Texto completo no disponible (Saber más ...)
• Resumen

  • We study Legendrian knots in a cabled knot type. Specifically, given a topological knot type K, we analyze the Legendrian knots in knot types obtained from K by cabling, in terms of Legendrian knots in the knot type 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 nontransversely- 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.