Strongly fillable contact structures without Liouville fillings

TL;DR

The paper develops a new technique to identify strongly fillable contact structures that lack Liouville fillings, expanding understanding of fillability obstructions in contact topology.

Contribution

It introduces a novel method to obstruct Liouville and weak fillability, demonstrating the existence of such structures on rational homology 3-spheres and extending previous results.

Findings

Certain rational homology 3-spheres admit strongly fillable contact structures without Liouville fillings

Extension of Ghiggini's results on Brieskorn spheres

Partial progress on a conjecture by Ghiggini and Van-Horn-Morris

Abstract

We introduce a new method to obstruct Liouville and weak fillability. Using this, we show that various rational homology 3-spheres admit strongly fillable contact structures without Liouville fillings, which extends the result of Ghiggini on a family of Brieskorn spheres. We also make partial progress on a conjecture of Ghiggini and Van-Horn-Morris.