Geometry/Topology Seminar
Tuesday September 17th, 2019
Time: 4:00 PM - 5:30 PM
Title: Desingularizing positive scalar curvature metrics on 4-manifolds
Speaker: Demetre Kazaras, Stony Brook University
Location: Math Tower P-131
We study 4-manifolds of positive scalar curvature (psc) with severe metric singularities along points and embedded circles, establishing a desingularization process based on work by Li-Mantoulidis in dimension 3. To carry this out, we show that the bordism group of closed 3-manifolds with psc metrics is trivial by explicit methods, using scalar-flat K{ä}hler ALE surfaces recently discovered by Lock-Viaclovsky. This allows us to prove a non-existence result for singular psc metrics on enlargeable 4-manifolds with uniformly Euclidian geometry. As a consequence, we obtain a low-regularity positive mass theorem for asymptotically flat 4-manifolds with non-negative scalar.