Cabling and transverse simplicity

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dc.creatorEtnyre, John B.
dc.creatorHonda, Ko
dc.date2003-06-23
dc.date2007-06-04
dc.date.accessioned2026-07-07T08:06:09Z
dc.date.available2026-07-07T08:06:09Z
dc.descriptionWe 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 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.
dc.description29 pages, published version
dc.identifierhttps://arxiv.org/abs/math/0306330
dc.identifierhttp://arxiv.org/abs/math/0306330
dc.identifierAnn. of Math. (2) 162 (2005), no. 3, 1305--1333
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130509
dc.subjectSymplectic Geometry
dc.subjectGeometric Topology
dc.subject53D10; 57M50; 57M25
dc.titleCabling and transverse simplicity
dc.typetext

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