Every Contact Manifolds can be given a Nonfillable Contact Structure

K. Niederkruger, O. van Koert
2010 International mathematics research notices  
Recently 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_-).
doi:10.1093/imrn/rnm115 fatcat:bshvhilaejhsppvfig6f3t4erm