Tight contact structures with no symplectic fillings

TL;DR

This paper constructs examples of tight contact structures on 3-manifolds that cannot be extended to symplectic fillings, highlighting limitations in the relationship between contact and symplectic topology.

Contribution

It provides explicit examples of tight contact structures lacking symplectic fillings, advancing understanding of contact topology boundaries.

Findings

Existence of tight contact structures without symplectic fillings

Counterexamples to fillability conjectures

Insights into contact and symplectic topology relationship

Abstract

We exhibit tight contact structures on 3-manifolds that do not admit any symplectic fillings.