• Corpus ID: 119121281

Notes on the octonions

@article{Salamon2010NotesOT,
  title={Notes on the octonions},
  author={Dietmar A. Salamon and Thomas Walpuski},
  journal={arXiv: Rings and Algebras},
  year={2010}
}
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 ${\rm Spin}(7)$. 
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In this article we introduce a method to construct $\rm{G}_2$-instantons on $\rm{G}_2$-manifolds arising from Joyce's generalised Kummer construction. The method is based on gluing ASD instantons
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