Work

Orientation-preserving homeomorphisms of Euclidean space are commutators

Year: 2025

Type: article

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.

Source: Proceedings of the American Mathematical Society Series B

DOI: 10.1090/bproc/258

Authors: Megha Bhat, Nicholas Vlamis

Institutions: The Graduate Center, CUNY, Queens College, CUNY

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $750

Funders: National Science Foundation, City University of New York