Title

Incompressible planar surfaces in 3-manifolds

Document Type

Article

Publication Date

1-1-1984

Abstract

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

First Page

121

Last Page

144

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