Quasi-actions whose quasi-orbits are quasi-isometric to trees

2023/05/22 by J. O. Button, Button, J. O. · 1 citation
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2305.13105

openalex publication_date 2023/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give necessary and sufficient conditions under which a quasi-action of any group on an arbitrary metric space can be reduced to a cobounded isometric action on some bounded valence tree, following a result of Mosher, Sageev and Whyte. Moreover if the quasi-action is metrically proper and quasi-orbits are quasi-isometric to trees then the group is virtually free.

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