Three-manifolds and Baumslag–Solitar groups

We show that the Baumslag–Solitar relation xn=yxmy−1 cannot hold in a nondegenerate way in the fundamental group of an orientable 3-manifold. This generalizes a result proved by Jaco and Shalen for the case of a Haken manifold. The generalization uses the general version of the Torus Theorem, the proof of which was completed by Casson and Jungreich and Gabai.