The conjugacy problem in Out(Fm) when the polynomial restrictions are non-growing

TL;DR

This paper proves the conjugacy problem in Out(Fm) is solvable for automorphisms with finite order restrictions on polynomial subgroups, using suspension structures and reduction techniques.

Contribution

It introduces a method to solve the conjugacy problem in Out(Fm) under polynomial restrictions of finite order, expanding understanding of automorphism structures.

Findings

Conjugacy problem is solvable for a specific class of automorphisms in Out(Fm).

Structural analysis of suspensions of free groups is key to the proof.

Reduction to group problems simplifies the conjugacy problem.

Abstract

We prove that the conjugacy problem in Out(Fm) is solvable for the class of outer automorphisms whose restrictions to their polynomial subgroups are of finite order. To do this, we first investigate the structure of suspensions of free groups by automorphisms whose outer class is of finite order. We then apply a reduction of our main result to certain problems on groups of this form.