Connected moduli of instantons on $S^3\times S^1$

TL;DR

This paper proves that the moduli space of $SU(2)$ instantons with charge $n$ on the manifold $S^3 imes S^1$ is connected, providing new insights into the topology of instanton moduli spaces.

Contribution

It establishes the connectedness of the moduli space of $SU(2)$ instantons on $S^3 imes S^1$, a result not previously known.

Findings

The moduli space $\\mathcal{M}_n$ is connected.

The proof involves topological and geometric analysis of instanton configurations.

This advances understanding of instanton moduli spaces on product manifolds.

Abstract

I prove connectedness of the moduli space $\mathcal M_n$ of $SU(2)$ instantons on $S^3\times S^1$ with charge $n$.