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.

arXiv commentThe 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

References in corpus (1)

• The vanishing of the contact invariant in the presence of torsion

Cited by in corpus (1)

• Classification of tight contact structures on surgeries on the figure-eight knot