Twisted local G-wild mapping class groups

Abstract: We consider the (universal) local isomonodromic deformations of irregular-singular connections defined on principal bundles over complex curves: for any (connected) complex reductive structure group G and any pole order, allowing for twisted/ramified formal normal forms at each pole and for twists in the interior of the curve. This covers the general case, and we particularly study the fundamental groups of the spaces of admissible deformations of irregular types/classes, in the viewpoint of (twisted/nonsplit) reflections cosets.