Incompressible planar surfaces in 3-manifolds
Let M be an orientable 3-manifold and T a torus component of ∂M. We show that the boundary-slopes of incompressible, boundary-incompressible planar surfaces (P,∂P)⊂(M,T) are pairwise within distance 4; in particular, there are at most six such boundary-slopes. A corollary is that, for any knot K in S3, at most six Dehn surgeries on K can yield a reducible 3-manifold. © 1984.
Publication Source (Journal or Book title)
Topology and its Applications
Gordon, C., & Litherland, R. (1984). Incompressible planar surfaces in 3-manifolds. Topology and its Applications, 18 (2-3), 121-144. https://doi.org/10.1016/0166-8641(84)90005-1