On the non-existence of tight contact structures

TL;DR

This paper demonstrates the existence of a specific 3-manifold that does not support any tight contact structures, highlighting limitations in the classification of contact structures.

Contribution

It provides a concrete example of a 3-manifold with no tight contact structures, advancing understanding of contact topology.

Findings

Existence of a 3-manifold with no tight contact structures

Counterexample to the universality of tight contact structures

Insights into the limitations of contact structure classification

Abstract

We exhibit a 3-manifold which admits no tight contact structure.