The conjugacy problem in groups of non-orientable 3-manifolds

TL;DR

This paper proves that the fundamental groups of non-orientable 3-manifolds have a solvable conjugacy problem by constructing an explicit algorithm, extending previous results to all geometrizable 3-manifolds.

Contribution

It establishes the solvability of the conjugacy problem for fundamental groups of non-orientable 3-manifolds, completing the classification for all geometrizable 3-manifold groups.

Findings

Solvable conjugacy problem for non-orientable 3-manifold groups

Algorithm construction for conjugacy problem

Extension of results to all geometrizable 3-manifolds

Abstract

We prove that fundamental groups of non-orientable 3-manifolds have a solvable conjugacy problem, and construct an algorithm. Together with our earlier work on the conjugacy problem in groups on orientable geometrizable 3-manifolds, all $\pi_1$ of (geometrizable) 3-manifolds have a solvable conjugacy problem. In corollaries, both the twisted conjugacy problem in closed surface groups and the conjugacy problem in closed surface-by-cyclic groups, are solvable.