Producing essential 2-spheres

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• 作者：Hoffman ; James A. ; Matignon ; Daniel
• 关键词：57N10 ; 57M25 ; 57M15 ; Dehn filling ; Intersection graphs ; Reducibility
• 刊名：Topology and its Applications
• 出版年：2002
• 期刊代码：60_01668641
• 类别：mt
• 出版时间：October 20, 2002
• 卷：124
• 期：3
• 页码：435-444
• 文件大小：92.4 K

摘要

Let M be an orientable 3-manifold M whose boundary is a torus, and which does not contain an essential 2-sphere. The goal is to minimize the number of slopes on the boundary of M which produce essential 2-spheres by Dehn filling, via their minimal geometric intersection number. Earlier papers in this direction are [Topology 35 (2) (1996) 395–409] and [Topology Appl. 43 (1992) 213–218]. In 1996, Gordon and Luecke proved in [Topology 35 (2) (1996) 395–409] that the slopes on the boundary of M intersect exactly once. They proved this using the representations of types which come from the intersection of planar graphs.