Microsheaf composition of Lagrangian correspondences
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908673460142080 |
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| author | Li, Wenyuan Nadler, David Shende, Vivek |
| author_facet | Li, Wenyuan Nadler, David Shende, Vivek |
| contents | In exact symplectic manifolds whose Liouville flow is gradientlike for a proper Morse function, one can associate conic microsheaves to eventually conic exact Lagrangians. Here we study how this 'microsheaf quantization' interacts with composition of Lagrangian correspondences. In particular: these operations commute when the composition is embedded. As an illustration, we show that Lie groups of exact symplectomorphisms act on microsheaf categories. The key technical advance is a version 'in families' of the gappedness criterion for commuting nearby cycles past tensor or Hom. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19814 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Microsheaf composition of Lagrangian correspondences Li, Wenyuan Nadler, David Shende, Vivek Symplectic Geometry In exact symplectic manifolds whose Liouville flow is gradientlike for a proper Morse function, one can associate conic microsheaves to eventually conic exact Lagrangians. Here we study how this 'microsheaf quantization' interacts with composition of Lagrangian correspondences. In particular: these operations commute when the composition is embedded. As an illustration, we show that Lie groups of exact symplectomorphisms act on microsheaf categories. The key technical advance is a version 'in families' of the gappedness criterion for commuting nearby cycles past tensor or Hom. |
| title | Microsheaf composition of Lagrangian correspondences |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2511.19814 |