Orientable maps and polynomial invariants of free-by-cyclic groups

Abstract

We relate the McMullen polynomial of a free-by-cyclic group to its Alexander polynomial. To do so, we introduce the notion of an orientable fully irreducible outer automorphism $\phi$ and use it to characterize when the homological stretch factor of $\phi$ is equal to its geometric stretch factor.

arXiv commentv2: 36 pages, 5 figures. Minor changes incorporating referee comments. Final version, to appear in Advances in Mathematics