Tight small Seifert fibered manifolds with $e_0=-2$

TL;DR

This paper classifies tight contact structures on certain small Seifert fibered manifolds and provides counterexamples to a question about the relationship between right-veering open books and tight contact structures.

Contribution

It offers a classification of tight contact structures on specific small Seifert fibered manifolds and constructs counterexamples to a conjecture linking right-veering open books to tightness.

Findings

Classified tight contact structures on small Seifert fibered manifolds with $e_0=-2$

Constructed infinitely many counterexamples to Honda-Kazez-Matic's question

Connected classification results with recent work by Lekili

Abstract

In this paper we provide the classification of tight contact structures on some small Seifert fibered manifolds. As an application of this classification, combined with work of Lekili in \cite{L2010}, we obtain infinitely many counterexamples to a question of Honda-Kazez-Mati\'{c} that asks whether a right-veering, non-destabilizable open book necessarily supports a tight contact structure.