Stabilization in the braid group II: Transversal simplicity of knots

The main result of this paper is a negative answer to the question: are all transversal knot types transversally simple? An explicit infinite family of examples is given of closed 3–braids that define transversal knot types that are not transversally simple. The method of proof is topological and indirect. 57M25; 57M50, 53C15 1 Introduction and description of results This paper is about knots which are transverse to the standard tight contact structure in R3, and about the ways in which topological information about braids can be used to learn new things about these ‘transversal knots’. Our approach to contact topology ha