Reducible and ∂-reducible Handle Additions
نویسندگان
چکیده
Let M be a simple 3-manifold with F a component of ∂M of genus at least two. For a slope α on F , we denote by M(α) the manifold obtained by attaching a 2-handle to M along a regular neighborhood of α on F . Suppose that α and β are two separating slopes on F such that M(α) and M(β) are reducible. Then the distance between α and β is at most 2. As a corollary, if g(F ) = 2, then there is at most one separating slope γ on F such that M(γ) is either reducible or ∂-reducible.
منابع مشابه
Boundary reducible handle additions on simple 3 - manifolds
Let M be a simple manifold, and F be a component of ∂M of genus two. For a slope γ on F , we denote by M(γ) the manifold obtained by attaching a 2-handle to M along a regular neighborhood of γ on F . In this paper, we shall prove that there is at most one separating slope γ on F so that M(γ) is ∂-reducible.
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تاریخ انتشار 2008