Non-smoothable homeomorphisms of $4$-manifolds with boundary
Geometric Topology
2025-02-27 v3 Differential Geometry
Abstract
We construct the first examples of non-smoothable self-homeomorphisms of smooth -manifolds with boundary that fix the boundary and act trivially on homology. As a corollary, we construct self-diffeomorphisms of -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.
Cite
@article{arxiv.2310.08666,
title = {Non-smoothable homeomorphisms of $4$-manifolds with boundary},
author = {Daniel Galvin and Roberto Ladu},
journal= {arXiv preprint arXiv:2310.08666},
year = {2025}
}
Comments
Minor modifications. To appear in Advances in Mathematics