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arXiv · 1607.05310

Quasi-invariant measures for some amenable groups acting on the line

Nancy Guelman·Cristóbal Rivas
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Abstract

In this note we show that if $G$ is a solvable group acting on the line, and if there is $T\in G$ having no fixed points, then there is a Radon measure $μ$ on the line quasi-invariant under $G$. In fact, our method allows for the same conclusion for $G$ inside a class of groups that is closed under extensions and contains all solvable groups and all groups of subexponential growth.

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Nancy Guelman, Cristóbal Rivas. 2016-07-18. Quasi-invariant measures for some amenable groups acting on the line. https://doi.org/10.2140/agt.2018.18.1067

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