English

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 (M,ξ)(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.

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