Incompressibility of Surfaces in Surgered 3-Manifolds
نویسنده
چکیده
The problem we consider in this paper was raised in [3]. Suppose T is a torus on the boundary of an orientable 3-manifold X, and S is a surface on ∂X − T which is incompressible in X. A slope γ is the isotopy class of a nontrivial simple closed curve on T . Denote by X(γ) the manifold obtained by attaching a solid torus to X so that γ is the slope of the boundary of a meridian disc. Given two slopes γ1 and γ2, we denote their (minimal) geometric intersection number by ∆(γ1, γ2).
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