Journal of Symplectic Geometry

Volume 18 (2020)

Number 6

Tight neighborhoods of contact submanifolds

Pages: 1629 – 1646



Luis Hernández–Corbato (Instituto de Ciencias Matematicas, Madrid, Spain)

Lucía Martín–Merchán (Departamento de Álgebra, Geometría y Topología, Universidad Complutense de Madrid, Spain)

Francisco Presas (Instituto de Ciencias Matematicas, Madrid, Spain)


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.

Received 30 March 2019

Accepted 16 March 2020

Published 2 February 2021