English

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 44-manifolds with boundary that fix the boundary and act trivially on homology. As a corollary, we construct self-diffeomorphisms of 44-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.

Keywords

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