Exactly fillable contact structures without Stein fillings

TL;DR

This paper presents examples of contact structures that can be exactly filled with symplectic forms but cannot be filled with Stein structures, addressing a specific open question in contact topology.

Contribution

It provides the first known examples of contact structures with exact symplectic fillings lacking Stein fillings, clarifying distinctions between these types of fillings.

Findings

Existence of contact structures with exact symplectic but no Stein fillings

Counterexamples to previous assumptions about fillability

Resolution of Ghiggini's question in contact topology

Abstract

We give examples of contact structures which admit exact symplectic fillings, but no Stein fillings, answering a question of Ghiggini.