Obstructions to smooth group actions on 4manifolds from families SeibergWitten theory
Seminar/Forum
213
Peter Hall
Monash Road
Let X be a smooth, compact, oriented 4manifold and consider the following problem. Let G be a group which acts on the second cohomology of X preserving the intersection form. Can this action of G on \(H^2(X)\) be lifted to an action of G on X by diffeomorphisms? We study a parametrised version of SeibergWitten theory for smooth families of 4manifolds and obtain obstructions to the existence of such lifts. For example, we construct compact simplyconnected 4manifolds X and involutions on \(H^2(X)\) that can be realised by a continuous involution on X, or by a diffeomorphism, but not by an involutive diffeomorphism for any smooth structure on X.
Presenter

David Baraglia, University of Adelaide