Non-smoothable homeomorphisms of 4-manifolds with boundary

Abstract

We construct the first examples of non-smoothable self-homeomorphisms of smooth 4-manifolds with boundary that fix the boundary and act trivially on homology. As a corollary, we construct self-diffeomorphisms of 4-manifolds with boundary that fix the boundary and act trivially on homology but cannot be isotoped to any self-diffeomorphism supported in a collar of the boundary and, in particular, are not isotopic to any generalised Dehn twist.