Explicit computation of the index of a positive outer automorphism of the free group

TL;DR

This paper presents a finite-time algorithm to compute the index of a positive outer automorphism of a free group, advancing the understanding of automorphism properties in algebraic structures.

Contribution

It introduces a novel algorithm for explicitly calculating the index of positive outer automorphisms of free groups, with proven finite termination.

Findings

Algorithm successfully computes the index in finite time.

Provides a method for analyzing automorphisms of free groups.

Enhances computational tools in algebraic topology.

Abstract

We give an algorithm for finding the index of a positive outer automorphism of the free group, and prove the algorithm exits in a finite time.