A gap theorem for half-conformally flat manifolds
A gap theorem for half-conformally flat manifolds
We show that a compact half-conformally flat manifold of negative type with bounded L2 energy, sufficiently small scalar curvature, and a noncollapsing assumption has all Betti numbers bounded in terms of the L2 curvature norm. We give examples of multi-ended bubbles that disrupt attempts to improve these Betti number bounds. …