The conjugacy problem in right-angled Artin groups and their subgroups

TL;DR

This paper demonstrates that the conjugacy problem in right-angled Artin groups and many of their natural subgroups can be efficiently solved in linear time, impacting computational group theory and related fields.

Contribution

It establishes a linear-time solution to the conjugacy problem in RAAGs and a broad class of their subgroups, including graph braid groups and groups from special cube complexes.

Findings

Conjugacy problem solvable in linear time for RAAGs

Extends linear-time solution to many subgroups, including hyperbolic groups

Includes fundamental groups of special cube complexes

Abstract

We prove that the conjugacy problem in right-angled Artin groups (RAAGs), as well as in a large and natural class of subgroups of RAAGs, can be solved in linear-time. This class of subgroups contains, for instance, all graph braid groups (i.e. fundamental groups of configuration spaces of points in graphs), many hyperbolic groups, and it coincides with the class of fundamental groups of ``special cube complexes'' studied independently by Haglund and Wise.