Hyperbolic immersions of free groups

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3 Scopus citations


We prove that the mapping torus of a graph immersion has a word-hyperbolic fundamental group if and only if the corresponding endomorphism does not produce Baumslag–Solitar subgroups. Due to a result by Reynolds, this theorem applies to all injective endomorphisms of F2 and nonsurjective fully irreducible endomorphisms of Fn.

Original languageEnglish (US)
Pages (from-to)1253-1275
Number of pages23
JournalGroups, Geometry, and Dynamics
Issue number4
StatePublished - 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


  • Combination theorem
  • Graph immersions
  • Nonsurjective endomorphisms
  • Word-hyperbolic


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