Bourgeois contact structures: Tightness, fillability and applications

Abstract Given a contact structure on manifold V together with supporting open book decomposition, Bourgeois gave an explicit construction of $$V \times {\mathbb {T}}^2$$ V × T 2 . We prove that all such structures are universally tight in dimension 5, independent whether the original is itself or overtwisted. In arbitrary dimensions, we provide obstructions to existence strong symplectic fillings manifolds. This gives broad class new examples weakly but not strongly fillable 5-manifolds, as well first odd dimensions. These particular instances more general for $${\mathbb {S}}^1$$ S 1 -invariant also obtain classification result namely unit cotangent bundle n -torus has unique symplectically aspherical filling up diffeomorphism.