Three-manifolds and Baumslag–Solitar groups

✍ Scribed by Peter B. Shalen

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 63 KB
• Volume: 110
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00167-4

✦ Synopsis

We show that the Baumslag-Solitar relation x n = yx m y -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.