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

Guelman, Nancy; Rivas, Cristóbal

doi:10.2140/agt.2018.18.1067

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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

DOI: 10.2140/agt.2018.18.1067

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 $μ$ 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.

Keywords

quasi-invariant measure, subexponential growth, amenable group, semiconjugacy

Mathematical Subject Classification 2010

Primary: 20F16, 28D15, 37C85, 57S25

References

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

Volume 18, issue 2 (2018)