TL;DR
This paper introduces a new family of groupoids over complex curves that act as universal domains for solutions to linear differential equations with singularities, enabling a functorial approach to resumming formal solutions.
Contribution
It constructs and describes Stokes groupoids that provide a universal and functorial framework for analyzing solutions to differential equations with singularities.
Findings
Universal domains for solutions to linear ODEs with singularities
Functorial method for resumming formal solutions
New insights into the structure of solution spaces
Abstract
We construct and describe a family of groupoids over complex curves which serve as the universal domains of definition for solutions to linear ordinary differential equations with singularities. As a consequence, we obtain a direct, functorial method for resumming formal solutions to such equations.
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