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Homogeneous actions on Urysohn spaces

Abstract : We show that many countable groups acting on trees, including free products of infinite 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 last author 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 infinite countable groups arises as a dense subgroup of the isometry group of the rational Urysohn space.
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https://hal.archives-ouvertes.fr/hal-03178570
Contributor : François Le Maître <>
Submitted on : Tuesday, March 23, 2021 - 9:54:16 PM
Last modification on : Thursday, April 15, 2021 - 3:08:17 PM

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  • HAL Id : hal-03178570, version 1
  • ARXIV : 1805.02477

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Pierre Fima, François Le Maître, Julien Melleray, Soyoung Moon. Homogeneous actions on Urysohn spaces. 2021. ⟨hal-03178570⟩

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