Four-dimensional generalized Ricci flows with nilpotent symmetry

We study solutions to generalized Ricci flow on four-manifolds with a nilpotent, codimension 1 symmetry. We show that. all such flows are immortal, and satisfy type III curvature and diameter estimates. Using a new kind of monotone energy adapted to this setting, we show that blowdown limits lie in a canonical finite-dimensional family of solutions. The results are new for Ricci flow.