Topology of Irregular Isomonodromy Times on a Fixed Pointed Curve

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.