Finiteness results for Heegaard surfaces in surgered manifolds
Finiteness results for Heegaard surfaces in surgered manifolds
复制标题
波动流形中 Heegaard 表面的有限性结果
DOI：
10.4310/cag.2001.v9.n2.a5
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发表时间：
2001
影响因子：
0.7
通讯作者：
E. Sedgwick
中科院分区：
文献类型：
--
作者：
Y. Rieck;E. Sedgwick
我们证明，除了有限数量的Dehn填充的尖流形上，所附的固体环面的核心是同位素到每个Heegaard表面的填充流形。此外，如果尖点流形不包含一个封闭的，非周边的，不可压缩的表面，然后在排除上述集合和那些填充的流形包含不可压缩的表面（也是一个有限集）后，每一个其他的流形由Dehn填充获得包含最多有限数量的Heegaard表面，这些表面不是尖点流形的Heegaard表面。由此可见，这些流形包含有限数目的有界亏格的Heegaard曲面。对于每个尖点流形，排除流形包含在一个有限的集合中，可以通过算法确定。
We demonstrate that for all but a finite number of Dehn fillings on a cusped manifold, the core of the attached solid torus is isotopic into every Heegaard surface for the filled manifold. Furthermore, if the cusped manifold does not contain a closed, non-peripheral, incompressible surface, then after excluding the aforementioned set and those filled manifolds containing incompressible surfaces (also a finite set) every other manifold obtained by Dehn filling contains at most a finite number of Heegaard surfaces that are not Heegaard surfaces for the cusped manifold. It follows that these manifolds contain a finite number of Heegaard surfaces of bounded genera. For each cusped manifold, the excluded manifolds are contained in a finite set that can be determined algorithmically.