McMullen polynomials and Lipschitz flows for free-by-cyclic groups

Spencer Dowdall, Ilya Kapovich, Christopher J. Leininger

Research output: Contribution to journalArticlepeer-review


Consider a group G and an epimorphism u0 V G→ Z inducing a splitting of G as a semidirect product ker(u0)Z with ker(u0) a finitely generated free group and ϵOut ker (u 0)representable by an expanding irreducible train track map. Building on our earlier work [DKL], in which we realized G as π1(X) for an Eilenberg-MacLane 2-complex X equipped with a semiflow , and inspired by McMullen's Teichmüller polynomial for fibered hyperbolic 3-manifolds, we construct a polynomial invariant mϵ ZTH1(G;Z)=torsionU for (X,) and investigate its properties [EQUATION PRESENTED].

Original languageEnglish (US)
Pages (from-to)3253-3353
Number of pages101
JournalJournal of the European Mathematical Society
Issue number11
StatePublished - 2017


  • BNS-Invariant
  • Free-By-Cyclic groups
  • Stretch Factors
  • Train Track Maps

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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