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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Free minimal actions of solvable Lie groups which are not affable
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by Fernando Alcalde Cuesta, Álvaro Lozano Rojo and Matilde Martínez PDF
Proc. Amer. Math. Soc. 149 (2021), 2679-2691 Request permission


We construct an uncountable family of transversely Cantor laminations of compact spaces defined by free minimal actions of solvable groups, which are not affable and whose orbits are not quasi-isometric to Cayley graphs.
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Additional Information
  • Fernando Alcalde Cuesta
  • Affiliation: Instituto de Matemáticas, Universidad de Santiago de Compostela, E-15782, Santiago de Compostela, Spain
  • MR Author ID: 24510
  • ORCID: 0000-0002-6863-4283
  • Email:
  • Álvaro Lozano Rojo
  • Affiliation: Centro Universitario de la Defensa, Academia General Militar, Ctra. Huesca s/n. E-50090 Zaragoza, Spain
  • ORCID: 0000-0002-1184-5901
  • Email:
  • Matilde Martínez
  • Affiliation: Instituto de Matemática y Estadística Rafael Laguardia, Facultad de Ingeniería, Universidad de la República, J.Herrera y Reissig 565, C.P.11300 Montevideo, Uruguay
  • ORCID: 0000-0002-4926-6892
  • Email:
  • Received by editor(s): December 5, 2019
  • Received by editor(s) in revised form: September 15, 2020
  • Published electronically: March 18, 2021
  • Additional Notes: This work was partially supported by Spanish MINECO Grant MTM2016-77642-C2-2-P), the European Regional Development Fund, and grant ANII-FCE-135352 from Uruguay.
    The research of the first author has been carried out despite the current administration of the University of Santiago de Compostela.

  • Dedicated: Dedicated to Jean Renault on his $70$th birthday
  • Communicated by: Nimish Shah
  • © Copyright 2021 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 2679-2691
  • MSC (2020): Primary 57R30; Secondary 37A20, 37B52
  • DOI:
  • MathSciNet review: 4246817