# Topology of the Stokes phenomenon

## TL;DR

The paper introduces a topological framework for understanding the Stokes phenomenon on complex algebraic curves, formalizing Stokes decompositions as an intermediate structure with a new characterization.

## Contribution

It formalizes Stokes decompositions and provides a novel, simplified characterization, bridging Stokes filtrations and local systems on algebraic curves.

## Key findings

- Formalization of Stokes decompositions as an intermediate category
- A new simple characterization of Stokes decompositions
- Enhanced understanding of connections on vector bundles on complex curves

## Abstract

Several intrinsic topological ways to encode connections on vector bundles on smooth complex algebraic curves will be described. In particular the notion of {\em Stokes decompositions} will be formalised, as a convenient intermediate category between the Stokes filtrations and the Stokes local systems/wild monodromy representations. The main result establishes a new simple characterisation of the Stokes decompositions.