Homogeneous actions on Urysohn spaces

Pierre Fima, François Le Maître, Julien Melleray, Soyoung Moon Colloquium Mathematicum MSC: Primary 03E15, 20E06; Secondary 20B22. DOI: 10.4064/cm7706-1-2021 Published online: 26 March 2021

Abstract

We show that many countable groups acting on trees, including free products of infinitely countable groups and surface groups, are isomorphic to dense subgroups of isometry groups of bounded Urysohn spaces. This extends previous results of the first and the last authors with Y. Stalder on dense subgroups of the automorphism group of the random graph. In the unbounded case, we also show that every free product of infinitely countable groups arises as a dense subgroup of the isometry group of the rational Urysohn space.

Authors

  • Pierre FimaUniversité de Paris, Sorbonne Université
    CNRS, Institut de Mathématiques
    de Jussieu – Paris Rive Gauche
    75013 Paris, France
    e-mail
  • François Le MaîtreUniversité de Paris, Sorbonne Université
    CNRS, Institut de Mathématiques
    de Jussieu – Paris Rive Gauche
    F-75013, Paris, France
    e-mail
  • Julien MellerayUniversité de Lyon
    Université Claude Bernard – Lyon 1
    CNRS UMR 5208, Institut Camille Jordan
    43 Boulevard du 11 novembre 1918
    69622 Villeurbanne Cedex, France
    e-mail
  • Soyoung MoonUniversité de Bourgogne
    Institut Mathématiques de Bourgogne
    CNRS UMR 5584
    BP 47870
    21078 Dijon Cedex, France
    e-mail

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