English

Non-regular Lagrangian concordances between Lagrangian fillable Legendrian knots

Symplectic Geometry 2025-09-18 v1

Abstract

In this short note, we construct a family of non-regular, and therefore non-decomposable, Lagrangian concordances between Lagrangian fillable Legendrian knots in the standard contact 3-dimensional sphere. More precisely, for every decomposable Lagrangian concordance from Λ\Lambda_- to Λ+\Lambda_+, where Λ±\Lambda_{\pm} are smoothly non-isotopic Legendrian knots, we construct a non-regular Lagrangian concordance from Λ+\Lambda'_+ to Λ\Lambda'_-, where both Λ±\Lambda'_\pm are Lagrangian fillable Legendrian knots obtained from Λ±\Lambda_{\pm} by sufficiently many positive and negative stabilisations, followed by a sequence of Legendrian satellite operations.

Keywords

Cite

@article{arxiv.2509.13594,
  title  = {Non-regular Lagrangian concordances between Lagrangian fillable Legendrian knots},
  author = {Georgios Dimitroglou Rizell and Roman Golovko},
  journal= {arXiv preprint arXiv:2509.13594},
  year   = {2025}
}

Comments

10 pages, 4 figures