Periodic monopoles and difference modules

TL;DR

This paper classifies a special class of periodic monopoles using algebraic difference modules, establishing a correspondence between geometric and algebraic structures, and analyzes their behavior at infinity.

Contribution

It introduces a classification of GCK-type periodic monopoles via difference modules with parabolic structure, linking differential geometry and algebraic methods.

Findings

Classification of GCK-type periodic monopoles via difference modules

Establishment of a Kobayashi-Hitchin type correspondence

Analysis of asymptotic behavior at infinity

Abstract

We study periodic monopoles satisfying some mild conditions, called of GCK type. Particularly, we give a classification of periodic monopoles of GCK type in terms of difference modules with parabolic structure, which is a kind of Kobayashi-Hitchin correspondence between differential geometric objects and algebraic objects. We also clarify the asymptotic behaviour of periodic monopoles of GCK type around infinity.