Through the analytic halo: Fission via irregular singularities

TL;DR

This paper explores the structure of moduli spaces of connections on bundles over Riemann surfaces with varying structure groups, generalizing complex character varieties as complex symplectic manifolds.

Contribution

It introduces a new framework for describing moduli spaces with irregular singularities as complex symplectic manifolds, extending existing theories.

Findings

Moduli spaces are described as complex symplectic manifolds.

Generalization of complex character varieties to irregular singularities.

Provides a geometric framework for variable structure groups.

Abstract

This article is concerned with moduli spaces of connections on bundles on Riemann surfaces, where the structure group of the bundle may vary in different regions of the surface. Here we will describe such moduli spaces as complex symplectic manifolds, generalising the complex character varieties of Riemann surfaces.