English

Tight contact structures on some plumbed 3-manifolds

Geometric Topology 2018-09-19 v2

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

R2 v1 2026-06-22T22:18:03.708Z