Notes on the octonions

Abstract

This is an expository paper. Its purpose is to explain the linear algebra that underlies Donaldson-Thomas theory and the geometry of Riemannian manifolds with holonomy in $G_2$ and $\mathrm{Spin}(7)$.

95 pages

References in corpus (1)

• K3 surfaces with non-symplectic involution and compact irreducible G_2-manifolds

Cited by in corpus (12)

• Introduction to ${\mathrm{G}}_2$ geometry
• General Relativity from Three-Forms in Seven Dimensions
• Asymptotically cylindrical manifolds with holonomy Spin(7). I
• Octonion-valued forms and the canonical 8-form on Riemannian manifolds with a $Spin(9)$-structure
• Deformation of singular connections I: $G_2-$instantons with point singularities
• The Mean Curvature of Special Lagrangian 3-folds in SU(3)-Structures with Torsion
• Spin(9) and almost complex structures on 16-dimensional manifolds
• A compact non-formal closed $G_2$ manifold with $b_1=1$
• On the Moduli Space of the Octonionic Nahm's Equations
• Integral geometry of exceptional spheres
• An integral formula for $G_2$-structures
• Local solution to the $G_2-$monopole equation with prescribed tangent cone and $G_2-$structure