Erratum: On iterated torus knots and transversal knots

Abstract

In [3] the author’s Theorems 1.1 and 1.2, combined, implied that iterated torus knots are transversally simple. This result is in error and this erratum pinpoints the error. In [4] a more subtle result is proven resulting in giving a geometric realization of the Honda‐Etnyre transverse (2,3)‐cable of the (2,3)‐torus knot example (appendix joint with H Matsuda). 57M27, 57N16; 57R17, 37F20 In [3] the author’s Theorems 1.1 and 1.2, combined, implied that iterated torus knots are transversally simple. The previous best result in this direction had been the proof, due to John Etnyre, that positive torus knots are transversally simple. After the publication of [3], Etnyre and Honda argued in [2], using very different techniques from those in [3], that among the infinitely many Legendrian knots whose topological knot type is that of the .3;2/‐cable on the .3;2/‐torus knot, there must be one whose transversal pushoff cannot be transversally simple. This lead to a review of the proof in [3] and the discovery of an error.