Submersions from Reducible Holonomy and $3$-$(\alpha,\delta)$-Sasaki Manifolds

We motivate the study of holonomy for connections with skew-symmetric torsion. I will then introduce a Riemannian submersion theorem via reducible holonomy representations of connections with skew torsion. After giving the general theorem I will discuss the most prominent example linking $3$-$(\alpha,\delta)$-Sasaki manifolds to quaternionic Kähler spaces.