Mapping class groups of simply connected 4-manifolds with boundary

Abstract

We compute the topological mapping class group of every compact, simply connected, topological 4-manifold. This was previously only known in the closed case. If the 4-manifold is smooth, we deduce an analogous description of the stable smooth mapping class group, extending work of Saeki.

v2 details new consequences of our results in the context of self-homeomorphisms that do not fix the boundary pointwise, and adds an appendix containing a recent new result of Auckly-Kronheimer-Ruberman. v3 incorporates referees' comments, and is the final version accepted for publication in JDG