Homotopy rigidity of nearby Lagrangian cocores
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914153670639616 |
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| author | Asplund, Johan Deshmukh, Yash Pieloch, Alex |
| author_facet | Asplund, Johan Deshmukh, Yash Pieloch, Alex |
| contents | An exact Lagrangian submanifold $L \subset X^{2n}$ in a Weinstein sector is called a nearby Lagrangian cocore if it avoids all Lagrangian cocores and is equal to a shifted Lagrangian cocore at infinity. Let $k$ be the dimension of the core of the subcritical part of $X$. For $n \geq 2k+2$ we prove that that the inclusion of $L$ followed by the retract to the Lagrangian core of $X$ and the quotient by the $(n-k-1)$-skeleton of the core, is null-homotopic. As a consequence, in many examples, a nearby Lagrangian cocore is smoothly isotopic (rel boundary) to a Lagrangian cocore in the complement of the missed Lagrangian cocores. The proof uses the spectral wrapped Donaldson-Fukaya category with coefficients in the ring spectrum representing the bordism group of higher connective covers of the orthogonal group. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_09548 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homotopy rigidity of nearby Lagrangian cocores Asplund, Johan Deshmukh, Yash Pieloch, Alex Symplectic Geometry Algebraic Topology Geometric Topology 57R58 53D12 An exact Lagrangian submanifold $L \subset X^{2n}$ in a Weinstein sector is called a nearby Lagrangian cocore if it avoids all Lagrangian cocores and is equal to a shifted Lagrangian cocore at infinity. Let $k$ be the dimension of the core of the subcritical part of $X$. For $n \geq 2k+2$ we prove that that the inclusion of $L$ followed by the retract to the Lagrangian core of $X$ and the quotient by the $(n-k-1)$-skeleton of the core, is null-homotopic. As a consequence, in many examples, a nearby Lagrangian cocore is smoothly isotopic (rel boundary) to a Lagrangian cocore in the complement of the missed Lagrangian cocores. The proof uses the spectral wrapped Donaldson-Fukaya category with coefficients in the ring spectrum representing the bordism group of higher connective covers of the orthogonal group. |
| title | Homotopy rigidity of nearby Lagrangian cocores |
| topic | Symplectic Geometry Algebraic Topology Geometric Topology 57R58 53D12 |
| url | https://arxiv.org/abs/2511.09548 |