#### Volume 18, issue 2 (2018)

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

### Nancy Guelman and Cristóbal Rivas

Algebraic & Geometric Topology 18 (2018) 1067–1076
##### Abstract

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 $\mu$ on the line quasi-invariant under $G\phantom{\rule{0.3em}{0ex}}$. 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.

##### Keywords
quasi-invariant measure, subexponential growth, amenable group, semiconjugacy
##### Mathematical Subject Classification 2010
Primary: 20F16, 28D15, 37C85, 57S25