Conjugacy problem in groups of non-oriented geometrizable 3-manifolds

TL;DR

This paper extends the proof of a solvable conjugacy problem from oriented to non-oriented geometrizable 3-manifold groups, completing the classification for all such manifolds.

Contribution

It proves that fundamental groups of non-oriented geometrizable 3-manifolds also have a solvable conjugacy problem, generalizing previous results.

Findings

Fundamental groups of non-oriented geometrizable 3-manifolds have a solvable conjugacy problem.

Completes the classification of 3-manifold groups with solvable conjugacy problem.

Extends previous work on oriented manifolds to include non-oriented cases.

Abstract

We have proved in [Topology, 45 1 (2006)] that fundamental groups of oriented geometrizable 3-manifolds have a solvable conjugacy problem. We now consider the case of groups of non-oriented geometrizable 3-manifolds in order to conclude that fundamental groups of geometrizable 3-manifolds all have a solvable conjugacy problem.