Haken spheres for genus two Heegaard splittings
Haken spheres for genus two Heegaard splittings
复制标题
哈肯球属的两个 Heegaard 分裂
DOI：
10.1017/s0305004117000718
复制
发表时间：
2018
影响因子：
0.8
通讯作者：
Yuya Koda
中科院分区：
文献类型：
--
作者：
Sangbum Cho;Yuya Koda
一个允许可约的属2偏裂的流形是3球、S2 × S1透镜空间或它们的连通和之一。对于每一个分裂，都定义了哈肯球的复合体。当流形为3球、S2 × S1或其和为透镜空间或S2 × S1的连通和时，一些作者研究了复形的组合结构。特别是，这些复合物都是可收缩的。在这项工作中，我们研究了剩余的情况，即当流形是透镜空间时。我们给出了一个精确的描述，每个复合体的属2 heegard分裂的透镜空间。一个值得注意的事实是，大多数透镜空间的复合体是不可收缩的，甚至是不相连的。
A manifold which admits a reducible genus-2 Heegaard splitting is one of the 3-sphere, S2 × S1, lens spaces or their connected sums. For each of those splittings, the complex of Haken spheres is defined. When the manifold is the 3-sphere, S2 × S1 or a connected sum whose summands are lens spaces or S2 × S1, the combinatorial structure of the complex has been studied by several authors. In particular, it was shown that those complexes are all contractible. In this work, we study the remaining cases, that is, when the manifolds are lens spaces. We give a precise description of each of the complexes for the genus-2 Heegaard splittings of lens spaces. A remarkable fact is that the complexes for most lens spaces are not contractible and even not connected.