Residually free 3-manifolds

TL;DR

This paper classifies certain 3-manifolds with incompressible toral boundary based on their residually free fundamental groups, revealing that prime, orientable cases are products of a surface and a circle.

Contribution

It provides a complete classification of compact 3-manifolds with incompressible toral boundary whose fundamental groups are residually free, identifying them as surface cross circle products.

Findings

Prime, orientable, non-trivial cases are surface times circle.

Fundamental groups of these manifolds are residually free.

Classification covers all such manifolds with the specified properties.

Abstract

We classify those compact 3-manifolds with incompressible toral boundary whose fundamental groups are residually free. For example, if such a manifold $M$ is prime and orientable and the fundamental group of $M$ is non-trivial then $M \cong \Sigma\times S^1$, where $\Sigma$ is a surface.