Non-nesting actions of groups on real trees vs isometric actions

2011/12/06 by A. Ivanov, А. А. Иванов, Ivanov, A.
Mathematics · #20E08 #Advanced Topology and Set Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR #msc:20E08

paper · pdf · doi:10.48550/arxiv.1112.1219

27 pages. arXiv admin note: substantial text overlap with arXiv:math/0607358

arxiv created 2011/12/06 · openalex publication_date 2011/12/06 · arxiv updated 2011/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study non-nesting actions on R-trees. We prove that some natural conditions describing how the group is generated, imply that such an action involves an isometric action on an R-tree. This can be applied to permutation groups, linear groups and some Polish groups.

Citations

• Non-nesting actions of Polish groups on pretrees

Related

• Non-nesting actions of Polish groups on pretrees
• Relative Rips Machine
• Actions of finitely generated groups on R-trees
• Finitely Presented Groups Acting on Trees
• Quasi-actions whose quasi-orbits are quasi-isometric to trees