Positive loops of loose Legendrian embeddings and applications

In this paper, we prove that there exist contractible positive loops of Legendrian embeddings based at any loose Legendrian submanifold. As an application, we define a partial order on $\widetilde{Cont}_0 (M, \xi)$, called strong orderability, and prove that overtwisted contact manifolds are not strongly orderable.

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Received 1 March 2017

Accepted 16 July 2019

Published 30 July 2020