Orientability of the moduli space of Spin(7)-instantons

Abstract

Let $(M,\Omega )$ be a closed $8$-dimensional manifold equipped with a generically non-integrable $\mathrm{Spin}(7)$-structure $\Omega$. We prove that if $\mathrm{Hom}(H^3(M,\mathbb{Z}),{\mathbb{Z}}_2)=0$ then the moduli space of irreducible $\mathrm{Spin}(7)$-instantons on $(M,\Omega )$ with gauge group $\mathrm{SU}(r)$, $r\ge 2$, is orientable.

To appear in Pure and Applied Mathematics Quarterly

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
• Deformation theory of deformed Donaldson-Thomas connections for $\mathrm{Spin}(7)$-manifolds