Characterising quasi-isometries of the free group

Antoine Goldsborough, Stefanie Zbinden

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Abstract

We introduce the notion of mixed subtree quasi-isometries, which are self-quasi-isometries of regular trees built in a specific inductive way. We then show that any self-quasi-isometry of a regular tree is at bounded distance from a mixed-subtree quasi-isometry. Since the free group is quasi-isometric to a regular tree, this provides a way to describe all self-quasi-isometries of the free group. In doing this, we also give a way of constructing quasi-isometries of the free group.

Original languageEnglish
Pages (from-to)5211-5219
Number of pages9
JournalAlgebraic and Geometric Topology
Volume24
Issue number9
DOIs
Publication statusPublished - 27 Dec 2024

Keywords

  • free group
  • geometric group theory
  • quasi-isometry

ASJC Scopus subject areas

  • Geometry and Topology

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