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Loose Legendrian embeddings in high dimensional contact manifolds
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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.
Forward citations
Cited by 4 Pith papers
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The h-principle fails for prelegendrians in corank 2 fat distributions
In corank-2 fat distributions, infinitely many prelegendrian tori share one formal class but are pairwise non-isotopic, detected by Legendrian contact homology of their canonical lifts.
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Non-orderability and the contact Hofer norm
Contact Hofer norm bounds, obtained from open books and loose Legendrians, imply non-orderability and resolve the standard S^1 × S^2 case.
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Lagrangian capacity and chain level string topology
The Lagrangian capacity of every convex or concave toric symplectic domain equals its diagonal, settling the Cieliebak–Mohnke ellipsoid conjecture and two related conjectures.
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Lagrangian concordance is not a partial order in high dimensions
In R^{4n+1} with n > 1, there exist pairs of non-isotopic loose Legendrian spheres with Lagrangian concordances in both directions, so Lagrangian concordance is not a partial order.
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