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

TL;DR

This paper explores the relationship between the McMullen polynomial and the Alexander polynomial in free-by-cyclic groups, introducing orientable automorphisms to analyze stretch factors.

Contribution

It introduces the concept of orientable fully irreducible outer automorphisms and characterizes conditions for equality of homological and geometric stretch factors.

Findings

McMullen polynomial related to Alexander polynomial in free-by-cyclic groups

Characterization of orientable fully irreducible automorphisms

Conditions for equality of homological and geometric stretch factors

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 $\varphi$ and use it to characterize when the homological stretch factor of $\varphi$ is equal to its geometric stretch factor.