2003/06/30 by John B. Etnyre, Ko Honda · 1 citation
Mathematics · #math.SG #math.GT #msc:53D10 #msc:57M50 #msc:57M25
published as Ann. of Math. (2) 162 (2005), no. 3, 1305--1333 · 29 pages, published version
arxiv created 2007/06/04 · arxiv updated 2009/11/30
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 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.