Transverse links, open books and overtwisted manifolds
Geometric Topology
2023-02-07 v2 Symplectic Geometry
Abstract
We prove that transverse links in any contact manifold 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.
Keywords
Cite
@article{arxiv.2108.07764,
title = {Transverse links, open books and overtwisted manifolds},
author = {Rima Chatterjee},
journal= {arXiv preprint arXiv:2108.07764},
year = {2023}
}
Comments
17 pages, 10 figures. Fixed the proof of theorem 1.2; lemma added; fixed some typos, to appear in NYJM