King’s Geometry seminar: Simon Salamon (King’s College London) - The Horrocks bundle as an instanton

The Horrocks bundle (not to be confused with the Horrocks-Mumford bundle) is an indecomposable holomorphic rank 3 bundle over CP^5 with c_2=3. It can be interpreted as a solution of the Yang-Mills equations on the quaternionic projective plane HP^2, via a Penrose transform and twistor equation.

In joint work with Udhav Fowdar, this realization leads to the existence of nowhere-vanishing spinors on HP^2 invariant by SU(3). Simon will use this example to introduce instantons associated with G-structures in higher dimensions, cohomogeneity-one actions by SU(3), and Spin(7) structures on 8-manifolds.