Burnside problem for measure preserving groups of toral homeomorphisms

Details Burnside problem for measure preserving groups of toral homeomorphisms Burnside problem for measure preserving groups of toral homeomorphisms

2011-08-18

arxiv.org/abs/1108.3778v1

Mathematics

Dynamical Systems

Scientific paper

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 $\mu$ is
finite. Moreover if the group consists in homeomorphisms isotopic to the
identity, then it is abelian and acts freely on $\mathbb{T}^2$.

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