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arXiv · 2511.19814

Microsheaf composition of Lagrangian correspondences

Wenyuan Li·David Nadler·Vivek Shende
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Abstract

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.

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Wenyuan Li, David Nadler, Vivek Shende. 2025-11-25. Microsheaf composition of Lagrangian correspondences. https://arxiv.org/abs/2511.19814

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