A gluing construction for periodic monopoles

TL;DR

This paper introduces a new method for constructing periodic monopoles with singularities on  olds using gluing techniques, advancing the understanding of monopole solutions in geometric analysis.

Contribution

It presents a novel gluing construction for periodic monopoles with singularities, expanding the toolkit for studying monopoles on non-compact manifolds.

Findings

Constructed explicit examples of periodic monopoles with singularities.

Developed a gluing method applicable to monopoles on  olds.

Enhanced the understanding of monopole moduli spaces with singularities.

Abstract

We construct periodic monopoles (with singularities), i.e. monopoles on $\mathbb{R}^{2} \times \mathbb{S}^{1}$ possibly singular at a finite collection of points, by gluing methods.