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Loose Legendrian embeddings in high dimensional contact manifolds

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arxiv 1201.2245 v5 pith:CDQ4MIL2 submitted 2012-01-11 math.SG

classification math.SG
keywords legendrianclasscontactdimensiondimensionalembeddingshighisotopy
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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.

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Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The h-principle fails for prelegendrians in corank 2 fat distributions

    math.SG 2025-11 conditional novelty 8.0 of 10

    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.

  2. Non-orderability and the contact Hofer norm

    math.SG 2024-11 conditional novelty 8.0 of 10

    Contact Hofer norm bounds, obtained from open books and loose Legendrians, imply non-orderability and resolve the standard S^1 × S^2 case.

  3. Lagrangian capacity and chain level string topology

    math.SG 2026-06 unverdicted novelty 7.0 of 10

    The Lagrangian capacity of every convex or concave toric symplectic domain equals its diagonal, settling the Cieliebak–Mohnke ellipsoid conjecture and two related conjectures.

  4. Lagrangian concordance is not a partial order in high dimensions

    math.SG 2024-11 conditional novelty 7.0 of 10

    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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