Stokes Structure and Direct Image of Irregular Singular $\mathcal D$-Modules

TL;DR

This paper introduces a topological approach to analyze the Stokes structure of specific irregular singular $ ext{D}$-modules, facilitating explicit computation of Stokes data for these complex mathematical objects.

Contribution

It provides a novel topological method to examine the Stokes structure of irregular singular $ ext{D}$-modules, especially for direct images of exponentially twisted regular singular connections.

Findings

Topological description of Stokes structure for certain $ ext{D}$-modules

Explicit computation of Stokes data in an example

Enhanced understanding of irregular singular $ ext{D}$-modules

Abstract

In this paper we will present a way of examining the Stokes structure of certain irregular singular $\mathcal D$-modules, namely the direct image of exponentially twisted regular singular meromorphic connections, in a topological point of view. This topological description enables us to compute Stokes data for an explicit example concretely.