Nonexistence and existence of fillable contact structures on 3-manifolds
Geometric Topology
2025-02-26 v3 Symplectic Geometry
Abstract
In the first part of this paper, we construct infinitely many hyperbolic closed 3-manifolds which admit no symplectic fillable contact structure. All these 3-manifolds are obtained by Dehn surgeries along L-space knots or L-space two-component links. In the second part of this paper, we show that Dehn surgeries along certain knots and links, including those considered in the first part, admit Stein fillable contact structures as long as the surgery coefficients are sufficiently large. This provides some new evidence for the high surgery conjecture raised by Stipsicz.
Keywords
Cite
@article{arxiv.2111.02151,
title = {Nonexistence and existence of fillable contact structures on 3-manifolds},
author = {Fan Ding and Youlin Li and Zhongtao Wu},
journal= {arXiv preprint arXiv:2111.02151},
year = {2025}
}
Comments
38 pages, 13 figures. Accepted version