A Whitehead algorithm for toral relatively hyperbolic groups

TL;DR

This paper presents an algorithmic solution to determine if a tuple of elements in a toral relatively hyperbolic group can be transformed into another tuple via automorphisms, advancing understanding of group automorphisms.

Contribution

The paper introduces a novel algorithm specifically designed for automorphic orbit problems in toral relatively hyperbolic groups, a class of groups with complex geometric properties.

Findings

Algorithm successfully determines automorphic orbit membership

Applicable to a broad class of toral relatively hyperbolic groups

Advances computational methods in geometric group theory

Abstract

We prove that there is an algorithm to determine whether a tuple of elements in a toral relatively hyperbolic group G is in the automorphic orbit of the other tuple.