Loose Legendrian embeddings in high dimensional contact manifolds

Abstract

We give an $h$--principle type result for a class of Legendrian embeddings in contact manifolds of dimension at least $5$. These Legendrians, referred to as loose, have trivial pseudo-holomorphic invariants. We demonstrate they are classified up to Legendrian isotopy by their smooth isotopy class equipped with an almost complex framing. This result is inherently high dimensional: analogous results in dimension $3$ are false.

References in corpus (2)

• Legendrian knots in overtwisted contact structures
• Flexible Weinstein manifolds

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