Spin(7)-instantons on Joyce's first examples of compact Spin(7)-manifolds

TL;DR

This paper introduces a novel construction of $Spin(7)$-instantons on Joyce's compact $Spin(7)$-manifolds, producing over 20,000 new instanton families across various structure groups using a gluing method.

Contribution

The authors develop a new method for constructing $Spin(7)$-instantons on Joyce's manifolds, differing from previous approaches, and generate a large family of explicit examples.

Findings

Constructed over 20,000 new $Spin(7)$-instantons.

Applied gluing techniques to combine local models and orbifold connections.

Produced instantons across multiple structure groups including $SO(3)$ to $SO(8)$.

Abstract

We construct $Spin(7)$-instantons on one of Joyce's compact $Spin(7)$-manifolds. The underlying compact $Spin(7)$-manifold given by Joyce is the same as in Lewis' construction of $Spin(7)$-instantons. However, our construction method and the resulting instantons are new. The compact $Spin(7)$-manifold is constructed by gluing a $Spin(7)$-orbifold and certain local model spaces around the orbifold singularities. We construct our instantons by gluing non-flat connections on the local model spaces to a flat connection on the $Spin(7)$-orbifold. We deliver more than $20,000$ new four-parameter families of examples of $Spin(7)$-instantons within the structure groups $SO(3), SO(4), SO(5), SO(7)$, and $SO(8)$.