English

Filtering the Heegaard Floer contact invariant

Geometric Topology 2019-05-08 v5 Symplectic Geometry

Abstract

We define an invariant of contact structures in dimension three from Heegaard Floer homology. This invariant takes values in the set Z0{}\mathbb{Z}_{\geq0}\cup\{\infty\}. It is zero for overtwisted contact structures, \infty for Stein fillable contact structures, non-decreasing under Legendrian surgery, and computable from any supporting open book decomposition. As an application, we obstruct Stein fillability on contact 3-manifolds with non-vanishing Ozsv\'ath-Szab\'o contact class.

Keywords

Cite

@article{arxiv.1603.02673,
  title  = {Filtering the Heegaard Floer contact invariant},
  author = {Cagatay Kutluhan and Gordana Matic and Jeremy Van Horn-Morris and Andy Wand},
  journal= {arXiv preprint arXiv:1603.02673},
  year   = {2019}
}

Comments

36 pages, 17 figures. This article supersedes arXiv:1503.01685v2. v5: Proposition 3.3 is replaced due to an error in its proof. Section 4 is modified accordingly. The contents of Section 5 are removed for future investigation. New application obstructing Stein fillability of contact 3-manifolds with non-vanishing Ozsvath-Szabo contact class is added as Section 5