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arXiv · 2211.03680

Tight contact structures without symplectic fillings are everywhere

Jonathan Bowden·Fabio Gironella·Agustin Moreno·Zhengyi Zhou
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Abstract

We show that for all $n \ge 3$, any $(2n+1)$-dimensional manifold that admits a tight contact structure, also admits a tight but non-fillable contact structure, in the same almost contact class. For $n=2$, we obtain the same result, provided that the first Chern class vanishes. We further construct Liouville but not Weinstein fillable contact structures on any Weinstein fillable contact manifold of dimension at least $7$ with torsion first Chern class.

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Jonathan Bowden, Fabio Gironella, Agustin Moreno, Zhengyi Zhou. 2022-11-07. Tight contact structures without symplectic fillings are everywhere. https://arxiv.org/abs/2211.03680

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