The microlocal Riemann-Hilbert correspondence for complex contact manifolds

TL;DR

This paper establishes a Riemann-Hilbert correspondence linking microlocalized D-modules and perverse microsheaves on complex contact manifolds, advancing the understanding of their categorical structures.

Contribution

It introduces a Riemann-Hilbert correspondence for complex contact manifolds, connecting microlocal D-modules with perverse microsheaves.

Findings

Categorical sheaf of microlocalized D-modules constructed on complex contact manifolds

Canonical notion of perverse microsheaves developed for these spaces

Riemann-Hilbert correspondence established between the two structures

Abstract

Kashiwara showed in 1996 that the categories of microlocalized D-modules can be canonically glued to give a sheaf of categories over a complex contact manifold. Much more recently, and by rather different considerations, we constructed a canonical notion of perverse microsheaves on the same class of spaces. Here we provide a Riemann-Hilbert correspondence.