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The singular support of sheaves is $\gamma$-coisotropic

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arxiv 2203.12977 v2 pith:WZ2UFXPT submitted 2022-03-24 math.SG math.AGmath.DG

Stéphane Guillermou , Claude Viterbo This is my paper · ORCID
classification math.SGmath.AGmath.DG
keywords gammacoisotropicprovesingularsupportinvariantinvolutivenumber
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abstract

We prove that the singular support of an element in the derived category of sheaves is $\gamma$-coisotropic, a notion defined in [Vit22]. We prove that this implies that it is involutive in the sense of Kashiwara-Schapira, but being $\gamma$-coisotropic has the advantage to be invariant by symplectic homeomorphisms (while involutivity is only invariant by $C^1$ diffeomorphisms) and we give an example of an involutive set that is not $\gamma$-coisotropic. Along the way we prove a number of results relating the singular support and the spectral norm $\gamma$ and raise a number of new questions.

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

    math.SG 2026-02 conditional novelty 7.0 of 10

    Iterated cones of cotangent fibers are dense in the filtered Fukaya category with respect to the interleaving distance, with a dim N + 1-cone improvement.

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