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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

We show that if G is a solvable group acting on the line and if there is T 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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quasi-invariant measure, subexponential growth, amenable group, semiconjugacy
Mathematical Subject Classification 2010
Primary: 20F16, 28D15, 37C85, 57S25
Received: 23 March 2017
Revised: 11 December 2017
Accepted: 21 December 2017
Published: 12 March 2018
Nancy Guelman
Instituto de Matemática y Estadistica Rafael Laguardia
Facultad de Ingeniería
Universidad de la República
Cristóbal Rivas
Departamento de Matemática y Ciencia de la Computación
Universidad de Santiago de Chile