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- W4309986727 abstract "Given a contact structure on a manifold $V$ together with a supporting open book decomposition, Bourgeois gave an explicit construction of a contact structure on $V times mathbb{T}^2$. We prove that all such structures are universally tight in dimension $5$, independent on whether the original contact manifold is itself tight or overtwisted. In arbitrary dimensions, we provide obstructions to the existence of strong symplectic fillings of Bourgeois manifolds. This gives a broad class of new examples of weakly but not strongly fillable contact $5$-manifolds, as well as the first examples of weakly but not strongly fillable contact structures in all odd dimensions. These obstructions are particular instances of more general obstructions for $mathbb S^1$-invariant contact manifolds. We also obtain a classification result in arbitrary dimensions, namely that the unit cotangent bundle of the $n$-torus has a unique symplectically aspherical strong filling up to diffeomorphism." @default.
- W4309986727 created "2022-11-30" @default.
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- W4309986727 date "2019-08-15" @default.
- W4309986727 modified "2023-09-30" @default.
- W4309986727 title "Bourgeois contact structures: tightness, fillability and applications" @default.
- W4309986727 doi "https://doi.org/10.48550/arxiv.1908.05749" @default.
- W4309986727 hasPublicationYear "2019" @default.
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