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Every contact manifold can be given a non-fillable contact structure

Klaus Niederkrüger·Otto van Koert
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Abstract

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_-).

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Klaus Niederkrüger, Otto van Koert. 2007-02-08. Every contact manifold can be given a non-fillable contact structure. https://doi.org/10.1093/imrn%2Frnm115

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