The local Laplace transform of an elementary irregular meromorphic connection

TL;DR

This paper introduces a topological approach to the local Laplace transform for certain differential systems, providing a method to compute the associated Stokes data for elementary irregular connections.

Contribution

It defines the topological local Laplace transform for Stokes-filtered local systems and computes the Stokes data of elementary differential systems in a topological manner.

Findings

Topological definition of the local Laplace transform for Stokes-filtered systems

Explicit computation of Stokes data for elementary irregular connections

Provides a new perspective on the analysis of irregular differential systems

Abstract

We give a definition of the topological local Laplace transformation for a Stokes-filtered local system on the complex affine line and we compute in a topological way the Stokes data of the Laplace transform of a differential system of elementary type.