On the existence of tight contact structures on Seifert fibered 3-manifolds

TL;DR

This paper characterizes which Seifert fibered 3-manifolds admit positive tight contact structures using a novel non-vanishing criterion for the contact Ozsváth-Szabó invariant.

Contribution

It introduces a new non-vanishing criterion for the contact Ozsváth-Szabó invariant to identify tight contact structures on Seifert fibered 3-manifolds.

Findings

Identifies all Seifert fibered 3-manifolds with positive tight contact structures

Develops a new criterion for the contact Ozsváth-Szabó invariant

Provides a classification tool for tight contact structures on these manifolds

Abstract

We determine the closed, oriented Seifert fibered 3-manifolds which carry positive tight contact structures. Our main tool is a new non-vanishing criterion for the contact Ozsvath-Szabo invariant.