Smoothing topological pseudo-isotopies of 4-manifolds
Geometric Topology
2025-07-24 v1
Abstract
Given a closed, smooth 4-manifold and self-diffeomorphism that is topologically pseudo-isotopic to the identity, we study the question of whether is moreover smoothly pseudo-isotopic to the identity. If the fundamental group of lies in a certain class, which includes trivial, free, and finite groups of odd order, we show the answer is always affirmative. On the other hand, we produce the first examples of manifolds and diffeomorphisms where the answer is negative. Our investigation is motivated by the question, which remains open, of whether there exists a self-diffeomorphism of a closed 4-manifold that is topologically isotopic to the identity, but not stably smoothly isotopic to the identity.
Cite
@article{arxiv.2507.16984,
title = {Smoothing topological pseudo-isotopies of 4-manifolds},
author = {Patrick Orson and Mark Powell and Oscar Randal-Williams},
journal= {arXiv preprint arXiv:2507.16984},
year = {2025}
}