Transverse links, open books and overtwisted manifolds

Rima Chatterjee

Published 2021-08-17Version 1

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 the coarse equivalence class of transverse link is zero if there is an overtwisted disk disjoint from it. Next, we find a relationship between the support genus of a Legendrian and transverse link and as a corollary show that a non-loose Legendrian knot will have non-loose transverse push-off if it has non-zero support genus.