$G_2$-instantons over twisted connected sums: an example

TL;DR

This paper constructs a specific example of a $G_2$-instanton on a twisted connected sum manifold, expanding the understanding of gauge theory in special holonomy geometries.

Contribution

It provides an explicit construction of an irreducible unobstructed $G_2$-instanton on a twisted connected sum, building on previous foundational work.

Findings

Explicit $G_2$-instanton example over twisted connected sum

Demonstrates unobstructed and irreducible properties of the instanton

Extends gauge theory applications in special holonomy manifolds

Abstract

Using earlier work of S\'a Earp and the author [SEW13] we construct an irreducible unobstructed $G_2$-instanton on an $\mathrm{SO}(3)$-bundle over a twisted connected sum recently discovered by Crowley-Nordstr\"om [CN14].