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Tight neighborhoods of contact submanifolds
Journal of Symplectic Geometry  (IF0.707),  Pub Date : 2020-12-01, DOI: 10.4310/jsg.2020.v18.n6.a4
Luis Hernández–Corbato, Lucía Martín–Merchán, Francisco Presas

We prove that any small enough neighborhood of a closed contact submanifold is always tight provided its normal bundle has a nowhere vanishing section. The non-existence of $\mathcal{C}^0$–small positive loops of contactomorphisms in general overtwisted manifolds is shown as a corollary.