Orientation-preserving homeomorphisms of Euclidean space are commutators
Geometric Topology
2024-12-30 v2
Abstract
We prove that every orientation-preserving homeomorphism of Euclidean space can be expressed as a commutator of two orientation-preserving homeomorphisms. We give an analogous result for annuli. In the annulus case, we also extend the result to the smooth category in the dimensions for which the associated sphere has a unique smooth structure. As a corollary, we establish that every orientation-preserving diffeomorphism of the real line is the commutator of two orientation-preserving diffeomorphisms.
Keywords
Cite
@article{arxiv.2311.00229,
title = {Orientation-preserving homeomorphisms of Euclidean space are commutators},
author = {Megha Bhat and Nicholas G. Vlamis},
journal= {arXiv preprint arXiv:2311.00229},
year = {2024}
}
Comments
v2: 13 pages, incorporates referee's comments, including a new discussion in the introduction detailing to what extent our arguments extend to diffeomorphisms. To appear in Proc. Am. Math. Soc