2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140650Recently Francisco Presas Mata constructed the first examples of closed contact manifolds of dimension larger than 3 that contain a plastikstufe, and hence are non-fillable. Using contact surgery on his examples we create on every sphere S^{2n-1}, n>1, an exotic contact structure ξ_- that also contains a plastikstufe. As a consequence, every closed contact manifold M (except S^1) can be converted into a contact manifold that is not (semi-positively) fillable by taking the connected sum of M with (S^{2n-1},ξ_-).15 pages, 4 figuresSymplectic GeometryGeometric Topology53D35; 57R17text