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

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.

v3: published version. Section 3 draws heavily from a corresponding section in arXiv:1205.5350

References in corpus (2)

• ${\mathrm{G}}_2$-instantons on generalised Kummer constructions
• A construction of Spin(7)-instantons

Cited by in corpus (3)

• Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-folds
• On orientations for gauge-theoretic moduli spaces
• Marginal deformations of heterotic $G_2$ sigma models