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arXiv · 2610.27686

Gauge theory on Cohomogeneity One Spin(7)-Manifolds from Aloff--Wallach Spaces

Hanci Chi·Enric Solé-Farré
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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.

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Hanci Chi, Enric Solé-Farré. 2026-10-20. Gauge theory on Cohomogeneity One Spin(7)-Manifolds from Aloff--Wallach Spaces. https://arxiv.org/abs/2610.27686

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