Digraphs and cycle polynomials for free-by-cyclic groups

Yael Algom-Kfir, Eriko Hironaka, Kasra Rafi

Research output: Contribution to journalArticlepeer-review


Letфε2 Out.Fn) be a free group outer automorphism that can be represented by an expanding, irreducible train-track map. The automorphism ф determines a freeby-cyclic group Г=Fnф Z and a homomorphism αεH1(Г;Z). By work of Neumann, Bieri, Neumann and Strebel, and Dowdall, Kapovich and Leininger, α has an open cone neighborhood A in H1(Г;∞) whose integral points correspond to other fibrations of Г whose associated outer automorphisms are themselves representable by expanding irreducible train-track maps. In this paper, we define an analog of McMullen’s Teichmüller polynomial that computes the dilatations of all outer automorphisms in A.

Original languageEnglish
Pages (from-to)1111-1154
Number of pages44
JournalGeometry and Topology
Issue number2
StatePublished - 10 Apr 2015

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ASJC Scopus subject areas

  • Geometry and Topology


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