Cubulating hyperbolic free-by-cyclic groups: The irreducible case

Mark F. Hagen, Daniel T. Wise

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

Let V be a finite graph, and let ϕ:V→V be an irreducible train track map whose mapping torus has word-hyperbolic fundamental group G. Then G acts freely and cocompactly on a CAT(0) cube complex. Hence, if F is a finite-rank free group and if Φ:F→F is an irreducible monomorphism so that G=F∗Φ is word-hyperbolic, then G acts freely and cocompactly on a CAT(0) cube complex. This holds, in particular, if Φ is an irreducible automorphism with G=F⋊ΦZ word-hyperbolic.
Original languageEnglish
Pages (from-to)1753-1813
Number of pages61
JournalDuke Mathematical Journal
Volume165
Issue number9
Early online date24 Mar 2016
DOIs
Publication statusPublished - 15 Jun 2016

Keywords

  • math.GR

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