Homeomorphism groups of commutator width one

Tsuboi, Takashi

doi:10.1090/S0002-9939-2012-11595-3

Homeomorphism groups of commutator width one
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Proc. Amer. Math. Soc. 141 (2013), 1839-1847 Request permission

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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