Tightness of Chekanov's bound on displacement energy for some Lagrangian knots
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915416573476864 |
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| author | Yaar, David Keren |
| author_facet | Yaar, David Keren |
| contents | By a classical theorem of Chekanov, the displacement energy, $e$, of a Lagrangian submanifold is bounded from below by the minimal area of pseudo-holomorphic disks with boundary on the Lagrangian, $\hbar$. We compute $e$ and $\hbar$ for displaceable Chekanov tori in $\mathbb{C}P^n$, and for an infinite family of exotic tori in $\mathbb{C}^3$ constructed by Brendel. In these families, $e=\hbar$.
We compare continuity properties of $e$ and $\hbar$ on the space of Lagrangians. This provides an example (suggested by Fukaya, Oh, Ohta, and Ono) where $e>\hbar$.
Our calculations have further applications such as a new proof, inspired by work of Auroux, that Brendel's family of exotic tori consists of infinitely many distinct Lagrangians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21282 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tightness of Chekanov's bound on displacement energy for some Lagrangian knots Yaar, David Keren Symplectic Geometry 53D12 (Primary) 53D20 (Secondary) By a classical theorem of Chekanov, the displacement energy, $e$, of a Lagrangian submanifold is bounded from below by the minimal area of pseudo-holomorphic disks with boundary on the Lagrangian, $\hbar$. We compute $e$ and $\hbar$ for displaceable Chekanov tori in $\mathbb{C}P^n$, and for an infinite family of exotic tori in $\mathbb{C}^3$ constructed by Brendel. In these families, $e=\hbar$. We compare continuity properties of $e$ and $\hbar$ on the space of Lagrangians. This provides an example (suggested by Fukaya, Oh, Ohta, and Ono) where $e>\hbar$. Our calculations have further applications such as a new proof, inspired by work of Auroux, that Brendel's family of exotic tori consists of infinitely many distinct Lagrangians. |
| title | Tightness of Chekanov's bound on displacement energy for some Lagrangian knots |
| topic | Symplectic Geometry 53D12 (Primary) 53D20 (Secondary) |
| url | https://arxiv.org/abs/2507.21282 |