HOMOGENEOUS ACTIONS ON URYSOHN SPACES
| Affiliation auteurs | !!!! Error affiliation !!!! |
| Titre | HOMOGENEOUS ACTIONS ON URYSOHN SPACES |
| Type de publication | Journal Article |
| Year of Publication | 2022 |
| Auteurs | Fima P, Le Maitre F, Melleray J, Moon S |
| Journal | COLLOQUIUM MATHEMATICUM |
| Volume | 167 |
| Pagination | 21-61 |
| Type of Article | Article |
| ISSN | 0010-1354 |
| Mots-clés | Baire category theorem, dense subgroups of Polish groups, group of finitely supported permutations, groups acting on trees, homogeneous action, Katetov extension, random graph, Urysohn space |
| Résumé | We show that many countable groups acting on trees, including free prod-ucts 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. |
| DOI | 10.4064/cm7706-1-2021 |