Instantons on multi-Taub-NUT spaces I: Asymptotic form and index theorem

Abstract

We study finite action anti-self-dual Yang–Mills connections on the multi-Taub-NUT space. Under a technical assumption of generic asymptotic holonomy, we establish the curvature and the harmonic spinor decay rates and compute the index of the associated Dirac operator.

This is the first in a series of papers proving the completeness of the bow construction of instantons on multi-Taub-NUT spaces and exploring it in detail.