The singular support of sheaves is γ-coisotropic

2022/03/24 by Guillermou, Stéphane, Claude Viterbo, Viterbo, Claude · 4 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2203.12977

openalex publication_date 2022/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the singular support of an element in the derived category of sheaves is γ-coisotropic, a notion defined in [Vit22]. We prove that this implies that it is involutive in the sense of Kashiwara-Schapira, but being γ-coisotropic has the advantage to be invariant by symplectic homeomorphisms (while involutivity is only invariant by C¹ diffeomorphisms) and we give an example of an involutive set that is not γ-coisotropic. Along the way we prove a number of results relating the singular support and the spectral norm γ and raise a number of new questions.

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• Proper kernels in microlocal sheaf theory
• C⁰-rigidity of Legendrians and coisotropics via sheaf quantization
• A remark on Continuous K-theory and Fourier-Sato transform
• An isometry theorem induced by the Radon transform between the convolution and interleaving distances

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