Uniform approximation of homeomorphisms by diffeomorphisms
Dynamical Systems
2016-07-28 v4 Differential Geometry
Abstract
We prove that a compactly supported homeomorphism of a smooth manifold of dimension greater or equal to 5 can be approximated uniformly by compactly supported diffeomorphisms if and only if it is isotopic to a diffeomorphism. If the given homeomorphism is in addition volume preserving, then it can be approximated uniformly by volume preserving diffeomorphisms.
Cite
@article{arxiv.0901.1002,
title = {Uniform approximation of homeomorphisms by diffeomorphisms},
author = {Stefan Müller},
journal= {arXiv preprint arXiv:0901.1002},
year = {2016}
}
Comments
v4: 5 pages; long overdue revision; clarified and improved statements, notation, and proofs. The main theorem may already be known, but I have not been able to find a precise reference. After talking to a number of topologists without getting a satisfactory answer, I decided to write up the proof myself. Comments and references welcome