Computing twisted conjugacy classes in free groups using nilpotent quotients

TL;DR

This paper introduces a novel algebraic algorithm leveraging nilpotent quotients to compute twisted conjugacy classes in free groups, surpassing traditional abelianization methods and applicable to related group settings.

Contribution

It presents a new technique for deciding twisted conjugacy using nilpotent quotients, improving success rates over existing methods.

Findings

The technique effectively computes twisted conjugacy classes in free groups.

Experimental results demonstrate high efficacy of the proposed method.

Applicability extends to surface groups and doubly twisted conjugacy.

Abstract

There currently exists no algebraic algorithm for computing twisted conjugacy classes in free groups. We propose a new technique for deciding twisted conjugacy relations using nilpotent quotients. Our technique is generalization of the common abelianization method, but admits significantly greater rates of success. We present experimental results demonstrating the efficacy of the technique, and detail how it can be applied the related settings of surface groups and doubly twisted conjugacy.