Pith. sign in

REVIEW 2 cited by

Instability of Legendrian knottedness, and non-regular Lagrangian concordances of knots

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2409.00290 v4 pith:EYGYNIHT submitted 2024-08-30 math.SG

classification math.SG
keywords legendrianknotslagrangianconcordanceshenceunknotanti-symmetricbesides
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We show that the family of smoothly non-isotopic Legendrian pretzel knots from the work of Cornwell-Ng-Sivek that all have the same Legendrian invariants as the standard unknot have front-spuns that are Legendrian isotopic to the front-spun of the unknot. Besides that, we construct the first examples of Lagrangian concordances between Legendrian knots that are not regular, and hence not decomposable. Finally, we show that the relation of Lagrangian concordance between Legendrian knots is not anti-symmetric, and hence does not define a partial order. The latter two results are based upon a new type of flexibility for Lagrangian concordances with stabilised Legendrian ends.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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

  1. 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.

  2. Non-decomposable Lagrangian cobordisms between Legendrian knots

    math.SG 2025-11 conditional novelty 6.0 of 10

    For every genus g>0, the authors build non-decomposable Lagrangian cobordisms of genus g between stabilized Legendrian knots, using Livingston's estimates to obstruct decomposability.

Pith tools