Solutions of the Bogomolny Equation on R^3 with Certain Type of Knot Singularity I

TL;DR

This paper investigates the moduli space of solutions to the Bogomolny equation on R^3 featuring knot singularities, aiming to connect gauge theory solutions with knot theory and low-dimensional topology.

Contribution

It introduces the study of Bogomolny equation solutions with knot singularities, extending the understanding of moduli spaces in gauge theory.

Findings

Analysis of moduli space structure with knot singularities

Potential applications in knot theory and low-dimensional topology

Foundation for future research on gauge solutions with singularities

Abstract

Moduli space of the Bogomolny equation on R^3 with certain asymptotic conditions at infinity has been well studied for a long time. This paper studies the moduli space of solutions to the Bogomolny equation on R^3 with a knot singularity. The author hopes such kind of moduli spaces have potential applications in low-dimensional topology and knot theory in the future.