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

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
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
##### Publication
Received: 23 March 2017
Revised: 11 December 2017
Accepted: 21 December 2017
Published: 12 March 2018
##### Authors
 Nancy Guelman Instituto de Matemática y Estadistica Rafael Laguardia Facultad de Ingeniería Universidad de la República Montevideo Uruguay Cristóbal Rivas Departamento de Matemática y Ciencia de la Computación Universidad de Santiago de Chile Santiago Chile