Gauge Theory in higher dimensions, II

Abstract

The main aim of the paper is to develop the "Floer theory" associated to Calabi-Yau 3-folds, exending the analogy of Thomas' "holomorphic Casson invariant". The treatment in the body of the paper is largely formal, assuming appropriate compactness properties of moduli spaces of $G_2$-instantons, but in the last section we make some remarks about these compactness isssues. Section 3 of the paper contains a general dscussion of deformations of the equations, for gauge field and submanifolds, associated to manifolds with exceptional holonomy.