The Heegaard distances cover all nonnegative integers
The Heegaard distances cover all nonnegative integers
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DOI：
10.2140/pjm.2015.275.231
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发表时间：
2013-02
影响因子：
0.6
通讯作者：
Ruifeng Qiu;Y. Zou;Qilong Guo
中科院分区：
文献类型：
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作者：
Ruifeng Qiu;Y. Zou;Qilong Guo
在本文中，我们证明了(1)对于任何整数 $n\geq 1$ 和 $g\geq 2$，有一个封闭的3-歧管 $M_{g}^{n}$ 它承认有距离 $n$ 属的侧面分裂 $g$ 除了这对 $(g, n)$ 是 $(2, 1)$． 此外， $M_{g}^{n}$ 可以选择双曲，除了这对 $(g, n)$ 是 $(3, 1)$． (2)对于任意整数 $g\geq 2$ 和 $n\geq 4$，存在无限多个允许距离的非同胚闭3流形 $n$ 属的边缘分裂 $g$．
In this paper, we prove that (1) For any integers $n\geq 1$ and $g\geq 2$, there is a closed 3-manifold $M_{g}^{n}$ which admits a distance $n$ Heegaard splitting of genus $g$ except that the pair of $(g, n)$ is $(2, 1)$. Furthermore, $M_{g}^{n}$ can be chosen to be hyperbolic except that the pair of $(g, n)$ is $(3, 1)$. (2) For any integers $g\geq 2$ and $n\geq 4$, there are infinitely many non-homeomorphic closed 3-manifolds admitting distance $n$ Heegaard splittings of genus $g$.