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arXiv · 2509.13594

Non-regular Lagrangian concordances between Lagrangian fillable Legendrian knots

Georgios Dimitroglou Rizell·Roman Golovko
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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 $\Lambda_-$ to $\Lambda_+$, where $\Lambda_{\pm}$ are smoothly non-isotopic Legendrian knots, we construct a non-regular Lagrangian concordance from $\Lambda'_+$ to $\Lambda'_-$, where both $\Lambda'_\pm$ are Lagrangian fillable Legendrian knots obtained from $\Lambda_{\pm}$ by sufficiently many positive and negative stabilisations, followed by a sequence of Legendrian satellite operations.

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Georgios Dimitroglou Rizell, Roman Golovko. 2025-09-16. Non-regular Lagrangian concordances between Lagrangian fillable Legendrian knots. https://arxiv.org/abs/2509.13594

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