Geodesic
McMullen polynomials and Lipschitz flows for free-by-cyclic groups
Journal of the European Mathematical Society, Tome 19 (2017) no. 11, pp. 3253-3353 Cet article a éte moissonné depuis la source EMS Press

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Consider a group G and an epimorphism u0​:G→Z inducing a splitting of G as a semidirect product ker(u0​)⋊φ​Z with ker(u0​) a finitely generated free group and φ∈ Out (ker(u0​)) 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 ψ, and inspired by McMullen's Teichmüller polynomial for fibered hyperbolic 3-manifolds, we construct a polynomial invariant m∈Z[H1​(G;Z)/torsion] for (X,ψ) and investigate its properties.
DOI : 10.4171/jems/739
Classification : 20-XX, 37-XX, 57-XX
Keywords: Free-by-cyclic groups, BNS-invariant, train track maps, stretch factors 
@article{JEMS_2017_19_11_a0,
     author = {Spencer Dowdall and Ilya Kapovich and Christopher J. Leininger},
     title = {McMullen polynomials and {Lipschitz} flows for free-by-cyclic groups},
     journal = {Journal of the European Mathematical Society},
     pages = {3253--3353},
     year = {2017},
     volume = {19},
     number = {11},
     doi = {10.4171/jems/739},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/739/}
}
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Spencer Dowdall; Ilya Kapovich; Christopher J. Leininger. McMullen polynomials and Lipschitz flows for free-by-cyclic groups. Journal of the European Mathematical Society, Tome 19 (2017) no. 11, pp. 3253-3353. doi: 10.4171/jems/739

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