On purely loxodromic actions

Ilya Kapovich

Research output: Contribution to journalArticle


We construct an example of an isometric action of F(a, b) on a δ-hyperbolic graph Y, such that this action is acylindrical, purely loxodromic, has asymptotic translation lengths of nontrivial elements of F(a, b) separated away from 0, has quasiconvex orbits in Y, but such that the orbit map F(a, b) → Y is not a quasi-isometric embedding.

Original languageEnglish (US)
Pages (from-to)89-101
Number of pages13
JournalMonatshefte fur Mathematik
Issue number1
StatePublished - Sep 1 2016


  • Acylindrical actions
  • Gromov-hyperbolic spaces
  • Quasi-isometric embeddings

ASJC Scopus subject areas

  • Mathematics(all)

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