Non-regular Lagrangian concordances between Lagrangian fillable Legendrian knots
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914041528582144 |
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| author | Rizell, Georgios Dimitroglou Golovko, Roman |
| author_facet | Rizell, Georgios Dimitroglou Golovko, Roman |
| contents | 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 $Λ_-$ to $Λ_+$, where $Λ_{\pm}$ are smoothly non-isotopic Legendrian knots, we construct a non-regular Lagrangian concordance from $Λ'_+$ to $Λ'_-$, where both $Λ'_\pm$ are Lagrangian fillable Legendrian knots obtained from $Λ_{\pm}$ by sufficiently many positive and negative stabilisations, followed by a sequence of Legendrian satellite operations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13594 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-regular Lagrangian concordances between Lagrangian fillable Legendrian knots Rizell, Georgios Dimitroglou Golovko, Roman Symplectic Geometry Primary 53D12, Secondary 53D42 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 $Λ_-$ to $Λ_+$, where $Λ_{\pm}$ are smoothly non-isotopic Legendrian knots, we construct a non-regular Lagrangian concordance from $Λ'_+$ to $Λ'_-$, where both $Λ'_\pm$ are Lagrangian fillable Legendrian knots obtained from $Λ_{\pm}$ by sufficiently many positive and negative stabilisations, followed by a sequence of Legendrian satellite operations. |
| title | Non-regular Lagrangian concordances between Lagrangian fillable Legendrian knots |
| topic | Symplectic Geometry Primary 53D12, Secondary 53D42 |
| url | https://arxiv.org/abs/2509.13594 |