Long turns, INP's and index for free group automorphisms

TL;DR

This paper introduces 'long turns', a new tool enhancing train track methods for free group automorphisms, enabling better control over periodic INPs and the automorphism's index.

Contribution

It presents a novel tool called 'long turns' that improves the analysis of automorphisms of free groups by controlling periodic INPs and the index.

Findings

'Long turns' effectively control periodic INPs.

The method improves understanding of automorphism indices.

Enhances train track technology for free group automorphisms.

Abstract

The goal of this paper is to introduce a new tool, called {\em long turns}, which is a useful addition to the train track technology for automorphisms of free groups, in that it allows one to control periodic INPs in a train track map and hence the index of the induced automorphism.