Density of fibers for the filtered Fukaya category of T^*N

2026/02/25 by Stéphane Guillermou, Claude Viterbo, Bingyu Zhang · 1 voice
Mathematics · #math.SG #math.CT

paper · pdf

arxiv published 2026/02/25 · arxiv updated 2026/06/01

Abstract

We answer a question of Biran and Cornea about the density of iterated cones of fibers in the Fukaya category of a cotangent bundle. We prove that indeed if we take a dense set of basepoints, the iterated cones of the cotangent fibres are dense in the Filtered Fukaya category. In an appendix we prove that the space of exact Lagrangians in a symplectic manifold is never totally bounded for the spectral distance (unless it is empty). This was implicit in \citeMCA-VH-CV for n=1 and proved for cotangent bundles of negatively curved manifolds in \citeA-B-C.

Citations

• Approximability for Lagrangian submanifolds
• C⁰-rigidity of Legendrians and coisotropics via sheaf quantization
• Almost mathematics, Persistence module, and Tamarkin category
• On the Hochschild cohomology of Tamarkin categories
• Filtered Fukaya categories
• On the Rouquier dimension of wrapped Fukaya categories and a conjecture of Orlov
• Gromov-Hausdorff distance between filtered A_∞ categories 1: Lagrangian Floer theory
• Sheaves and symplectic geometry of cotangent bundles
• Sectorial descent for wrapped Fukaya categories
• Persistence-like distance on Tamarkin's category and symplectic displacement energy
• Covariantly functorial wrapped Floer theory on Liouville sectors
• Simplicial nerve of an A-infinity category
• Sheaf quantization of Hamiltonian isotopies and applications to non displaceability problems

Discussions

• St\'ephane Guillermou, Claude Viterbo, Bingyu Zhang: Density of fibers for the filtered Fukaya category of $T^*N$ https://arxiv.org/abs/2602.21759 https://arxiv.org/pdf/2602.21759 https://arxiv.org/ht [bsky, 0 points, 0 comments]

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