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

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].