Transverse links, open books and overtwisted manifolds

Abstract

We prove that transverse links in any contact manifold $(M,\xi )$ can be realized as a sub-binding of a compatible open book decomposition. We define the support genus of a transverse link and prove that the support genus of a transverse knot is zero if there is an overtwisted disk disjoint from it. Next, we find a relationship between the support genus of a transverse link and its Legendrian approximation.

17 pages, 10 figures. Fixed the proof of theorem 1.2; lemma added; fixed some typos, to appear in NYJM

References in corpus (2)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• On the equivalence of Legendrian and transverse invariants in knot Floer homology