${\mathrm{G}}_2$-instantons on the 7-sphere

Abstract

We study the deformation theory of ${\mathrm{G}}_2$-instantons on the 7-sphere, specifically those obtained from instantons on the 4-sphere via the quaternionic Hopf fibration. We find that the pullback of the standard ASD instanton lies in a smooth, complete, 15-dimensional family of ${\mathrm{G}}_2$-instantons. In general, the space of infinitesimal ${\mathrm{G}}_2$-instanton deformations on $S^7$ is identified with three copies of the space of ASD deformations on $S^4.$

Final version, appeared in JLMS

Cited by in corpus (2)

• Deformations of ${\mathrm{G}}_2$-instantons on nearly ${\mathrm{G}}_2$ manifolds
• Families of solutions of the heterotic G${}_2$ system