Topology Seminar
April 8, 2-3 PM, Nelson Room
Alexander Kupers, U of Toronto

Title: A parametrised sum-stable smoothing theorem for topological 4-manifolds
Abstract: The sum-stable smoothing theorem of Freedman and Quinn implies that if the topological tangent manifold of a topological 4-manifold admits a refinement to a vector bundle, then the 4-manifold admits a smooth structure after finitely many connected sums with S^2 x S^2. We generalise this to families of topological 4-manifolds, though in a weaker form than higher-dimensional smoothing theory: we prove that a space of smooth structures, stabilised at varying locations, is homology equivalent to a space of vector bundle refinements of the topological tangent bundle, stabilised at varying locations. I will explain the statement, proof strategy, and some interesting consequences. This is joint work with Christian Kremer.