Orientation-preserving homeomorphisms of Euclidean space are commutators

Megha Bhat; Nicholas Vlamis

doi:10.1090/bproc/258

journal article Open Access Apr 25, 2025

Orientation-preserving homeomorphisms of Euclidean space are commutators

Proceedings of the American Mathematical Society, Series B Vol. 12 No. 4 pp. 38-47 · American Mathematical Society (AMS)

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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.

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Details

Published: Apr 25, 2025
Vol/Issue: 12(4)
Pages: 38-47
License: View

Authors

Funding

National Science Foundation Award: 2212922

Cite This Article

Megha Bhat, Nicholas Vlamis (2025). Orientation-preserving homeomorphisms of Euclidean space are commutators. Proceedings of the American Mathematical Society, Series B, 12(4), 38-47. https://doi.org/10.1090/bproc/258

Orientation-preserving homeomorphisms of Euclidean space are commutators

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