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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Homeomorphism groups of commutator width one


Author: Takashi Tsuboi
Journal: Proc. Amer. Math. Soc. 141 (2013), 1839-1847
MSC (2010): Primary 54H15, 54H20, 57S05; Secondary 20F65, 37B05, 57N50
Published electronically: November 28, 2012
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Abstract: We show that any element of the identity component $ \mathrm {Homeo}(S^n)_0$ of the group of homeomorphisms of the $ n$-dimensional sphere $ S^n$ can be written as one commutator. We also show that any element of the group $ \mathrm {Homeo}(\mu ^n)$ of homeomorphisms of the $ n$-dimensional Menger compact space $ \mu ^n$ can be written as one commutator.


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Additional Information

Takashi Tsuboi
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, Komaba Meguro, Tokyo 153-8914, Japan
Email: tsuboi@ms.u-tokyo.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11595-3
PII: S 0002-9939(2012)11595-3
Keywords: Homeomorphism group, uniformly perfect, commutator subgroup
Received by editor(s): September 12, 2011
Published electronically: November 28, 2012
Additional Notes: The author is partially supported by Grant-in-Aid for Scientific Research (A) 20244003, (S) 24224002, Grant-in-Aid for Exploratory Research 21654009, 24654011, Japan Society for Promotion of Science, and by the Global COE Program at the Graduate School of Mathematical Sciences, University of Tokyo.
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.