Let \phi \in \mbox{Out}(F_n) be a free group outer automorphism that can be
represented by an expanding, irreducible train-track map. The automorphism
ϕ determines a free-by-cyclic group Γ=Fn​⋊ϕ​Z,
and a homomorphism α∈H1(Γ;Z). By work of Neumann,
Bieri-Neumann-Strebel and Dowdall-Kapovich-Leininger, α has an open cone
neighborhood A in H1(Γ;R) whose integral points
correspond to other fibrations of Γ whose associated outer automorphisms
are themselves representable by expanding irreducible train-track maps. In this
paper, we define an analog of McMullen's Teichm\"uller polynomial that computes
the dilatations of all outer automorphism in A.Comment: 41 pages, 20 figure