Tight contact structures on some plumbed 3-manifolds
Abstract
In this article, we prove a generalization of a theorem of Lisca-Matic to Stein cobordisms and develop a method for distinguishing certain Stein cobordisms using rotation numbers. Using these results along with standard techniques from convex surface theory and classifications of tight contact structures on certain 3-manifolds due to Honda, we classify the tight contact structures on a certain class of plumbed 3-manifolds that bound non-simply connected 4-manifolds. Moreover, we give descriptions of the Stein fillings of the Stein fillable contact structures.
Keywords
Cite
@article{arxiv.1710.06702,
title = {Tight contact structures on some plumbed 3-manifolds},
author = {Jonathan Simone},
journal= {arXiv preprint arXiv:1710.06702},
year = {2018}
}
Comments
The first version of this paper only considered tight contact structures with no Giroux torsion on certain plumbed 3-manifolds. This updated version classifies all tight contact structures on such 3-manifolds