Strongly fillable contact structures without Liouville fillings

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.

arXiv comment20 pages, 3 figures. Updates on weak fillings