Spin(7)-instantons, Cayley submanifolds, and Fueter sections

TL;DR

This paper establishes an existence theorem for Spin(7)-instantons concentrated near Cayley submanifolds and demonstrates their construction on Spin(7)-manifolds with K3 Cayley fibrations, extending previous results.

Contribution

It provides a new existence theorem for Spin(7)-instantons near Cayley submanifolds and constructs examples on manifolds with K3 Cayley fibrations, partially reversing Tian's compactness theorem.

Findings

Proved existence of Spin(7)-instantons near Cayley submanifolds

Constructed Spin(7)-instantons on manifolds with K3 Cayley fibrations

Recovered an example previously constructed by Lewis

Abstract

We prove an existence theorem for Spin(7)-instantons, which are highly concentrated near a Cayley submanifold; thus giving a partial converse to Tian's foundational compactness theorem. As an application, we show how to construct Spin(7)-instantons on Spin(7)-manifolds with suitable local K3 Cayley fibrations. This recovers an example constructed by Lewis.