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

TL;DR

This paper establishes that the singular support of sheaves is $ extgamma$-coisotropic, a property invariant under symplectic homeomorphisms, and explores its implications and distinctions from involutivity.

Contribution

It introduces the notion of $ extgamma$-coisotropic singular support, proves its invariance under symplectic homeomorphisms, and compares it with involutivity, providing new insights and questions.

Findings

Singular support is $ extgamma$-coisotropic.

$ extgamma$-coisotropic implies involutive.

Example of involutive set not $ extgamma$-coisotropic.

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.