3-Manifolds as viewed from the curve complex ☆
3-Manifolds as viewed from the curve complex ☆
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DOI：
10.1016/s0040-9383(00)00033-1
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发表时间：
1997-12
期刊：
影响因子：
--
通讯作者：
J. Hempel
中科院分区：
文献类型：
--
作者：
J. Hempel
将三维流形的Heegaard图看作是曲面上曲线复形中的一对单形，将Heegaard分裂看作是由等价图生成的一对子复形。我们与这些子复形的拓扑性质的流形和/或相关的分裂的几何和组合性质。例如，我们表明，对于任何分裂的3-流形，这是塞弗特纤维或其中包含一个本质环面的子复形是在一个距离最多为两个分开的单纯距离的曲线复杂;而有分裂，其中的子复形是任意远。我们也给障碍，计算从一个给定的图，被塞弗特纤维或包含一个重要的环面。
A Heegaard diagram for a 3-manifold is regarded as a pair of simplexes in the complex of curves on a surface and a Heegaard splitting as a pair of subcomplexes generated by the equivalent diagrams. We relate geometric and combinatorial properties of these subcomplexes with topological properties of the manifold and/or the associated splitting. For example we show that for any splitting of a 3-manifold which is Seifert fibered or which contains an essential torus the subcomplexes are at a distance at most two apart in the simplicial distance on the curve complex; whereas there are splittings in which the subcomplexes are arbitrarily far apart. We also give obstructions, computable from a given diagram, to being Seifert fibered or to containing an essential torus.