September 11, 2018
TITLE: Canonical Orientations for the Moduli Space of G2-instantons
ABSTRACT: The moduli space of anti-self-dual connections for 4-manifolds has been generalized by Donaldson-Segal to special, higher-dimensional geometries. I will discuss a technique for fixing canonical orientations on these moduli spaces in dimension 7 and for the gauge group SU(n). These orientations depend on the choice of a flag structure, an additional piece of data on the underlying 7-manifold introduced by Joyce. After discussing the reconstruction of an SU(n)-bundle from its ‘Poincaré dual’ submanifold, the definition of canonical orientations will be presented, based on the excision principle from index theory.