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arXiv · 1108.3778

Burnside problem for measure preserving groups of toral homeomorphisms and for 2-groups of toral homeomorphisms

Nancy Guelman·Isabelle Liousse
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Abstract

A group $G$ is said to be periodic if for any $g\in G$ there exists a positive integer $n$ with $g^n=id$. We prove that a finitely generated periodic group of homeomorphisms on the 2-torus that preserves a measure $μ$ is finite. Moreover if the group consists in homeomorphisms isotopic to the identity, then it is abelian and acts freely on $\mathbb{T}^2$. In the Appendix, we show that every finitely generated 2-group of toral homeomorphisms is finite.

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Nancy Guelman, Isabelle Liousse. 2014-04-04. Burnside problem for measure preserving groups of toral homeomorphisms and for 2-groups of toral homeomorphisms. https://arxiv.org/abs/1108.3778

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