Topology of irregular isomonodromy times on a fixed pointed curve

TL;DR

This paper explores the structure of deformation spaces of irregular classes on Riemann surfaces, aiming to understand their fundamental groups and generalize G-braid groups in the context of irregular isomonodromy systems.

Contribution

It introduces a new framework for studying deformation spaces of irregular classes and extends the concept of G-braid groups to these settings.

Findings

Defined moduli spaces of irregular class deformations

Analyzed the fundamental groups of these spaces

Proposed a generalization of G-braid groups

Abstract

We will define and study (moduli) spaces of deformations of irregular classes on Riemann surfaces, which provide an intrinsic viewpoint on the `times' of irregular isomonodromy systems in general. Our aim is to study the deeper generalisation of the G-braid groups that occur as fundamental groups of such deformation spaces, with particular focus on the generalisation of the full G-braid groups.