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Bourgeois' contact manifolds are tight

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arxiv 2404.16311 v1 pith:QG7ACJCW submitted 2024-04-25 math.SG

Russell Avdek , Zhengyi Zhou This is my paper · ORCID
classification math.SG
keywords contactbourgeoisstructurestightalwaysbookscomputationdetermined
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abstract

We prove that Bourgeois' contact structures on $M \times \mathbb{T}^{2}$ determined by the supporting open books of a contact manifold $(M, \xi)$ are always tight. The proof is based on a contact homology computation leveraging holomorphic foliations and Kuranishi structures.

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  1. Unknottedness of symplectic submanifold fillings

    math.SG 2025-06 conditional novelty 6.0 of 10

    Symplectic fillings of the standard codimension-2 contact sphere in a symplectic ball are smoothly isotopic to the standard linear disk.

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