On the parametrised Whitehead torsion of families of nearby Lagrangian submanifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908396496617472 |
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| author | Courte, Sylvain Porcelli, Noah |
| author_facet | Courte, Sylvain Porcelli, Noah |
| contents | Motivated by the strong nearby Lagrangian conjecture, we constrain the parametrised Whitehead torsion of a family of closed exact Lagrangian submanifolds in a cotangent bundle. We prove the parametrised Whitehead torsion admits a factorisation through simpler maps, in particular implying it is trivial on $π_0$, $π_1$, and that its image is divisible by the Euler characteristic. We provide concrete implications for the Lagrangian monodromy question in the case of a high dimensional torus.
This generalises earlier work of Abouzaid and Kragh \cite{AbKr} on the $π_0$ version, using different methods. Our main tool is the theory of twisted generating functions, building on \cite{ACGK}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06110 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the parametrised Whitehead torsion of families of nearby Lagrangian submanifolds Courte, Sylvain Porcelli, Noah Symplectic Geometry Algebraic Topology K-Theory and Homology Motivated by the strong nearby Lagrangian conjecture, we constrain the parametrised Whitehead torsion of a family of closed exact Lagrangian submanifolds in a cotangent bundle. We prove the parametrised Whitehead torsion admits a factorisation through simpler maps, in particular implying it is trivial on $π_0$, $π_1$, and that its image is divisible by the Euler characteristic. We provide concrete implications for the Lagrangian monodromy question in the case of a high dimensional torus. This generalises earlier work of Abouzaid and Kragh \cite{AbKr} on the $π_0$ version, using different methods. Our main tool is the theory of twisted generating functions, building on \cite{ACGK}. |
| title | On the parametrised Whitehead torsion of families of nearby Lagrangian submanifolds |
| topic | Symplectic Geometry Algebraic Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2506.06110 |