In this article we present infinitely many 3–manifolds admitting infinitely many universally tight contact structures each with trivial Ozsváth–Szabó contact invariants. By known properties of these invariants the contact structures constructed here are non weakly symplectically fillable.
"Infinitely many universally tight contact manifolds with trivial Ozsváth–Szabó contact invariants." Geom. Topol. 10 (1) 335 - 357, 2006. https://doi.org/10.2140/gt.2006.10.335