Year: 2026
Type: preprint
Abstract: We begin a systematic study of $\mathrm{Spin}(7)$-instantons on complete non-compact cohomogeneity one $\mathrm{Spin}(7)$-manifolds with Aloff--Wallach spaces $N_{k,l}=\mathrm{SU}(3)/\mathrm{U}(1)_{k,l}$ as principal orbits. We provide a complete classification of admissible principal $\mathrm{U}(1)$- and $\mathrm{SO}(3)$-bundles and smooth bounded solutions to the $\mathrm{Spin}(7)$-instanton equation on them. We study bubbling phenomena for the constructed $\mathrm{Spin}(7)$-instantons and discuss the compactification of the moduli space of $\mathrm{Spin}(7)$-instantons in both the ALC and AC settings.
Source: arXiv (Cornell University)
Authors: Chi, Hanci, Solé-Farré, Enric
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223119908