Notes on the octonians

Abstract

In these notes we give an exposition of the structures in linear algebra that underlie Donaldson-Thomas theory [2, 3] and calibrated geometry [4, 5]. No claim is made to originality. All the results and ideas described here (except perhaps Theorem 7.4) can be found in the existing literature, notably in the beautiful paper [4] by Harvey and Lawson. Perhaps these notes might be a useful introduction for students who wish to enter the subject.