Heegaard structures of manifolds in the Dehn filling space
Heegaard structures of manifolds in the Dehn filling space
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Dehn 填充空间中流形的 Heegaard 结构
DOI：
10.1016/s0040-9383(99)00026-9
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
Y. Rieck
中科院分区：
文献类型：
--
作者：
Y. Rieck
我们证明了在一个圆柱形三维流形的边界上，当Dehn填充了一个不可压缩环面后，Heegaard亏格最多退化一个。我们这样做是通过证明，所有，但1000填充的核心所附的固体环面可以同位素到最小Heegaard表面的填充流形，我们说，这些流形是好的。对于这些填充，在稳定Heegaard曲面一次之后，它就变成了原始流形的Heegaard曲面。我们表明，任何两个Heegaard表面在不同的填充物，其中的核心是不是同位素，可以同位素相交基本上。利用这一点，一个边界上的填充包含这样的表面之间的距离给出的Heegaard表面的属。
We prove that after Dehn filling an incompressible torus in the boundary of an a-cylindrical 3-manifold the Heegaard genus degenerates by at most one for all but finitely many fillings. We do so by proving that for all but finitely many fillings the core of the attached solid torus can be isotoped into the minimal Heegaard surface of the filled manifold, we say that these manifolds are good. For these fillings, after stabilizing the Heegaard surface once, it becomes a Heegaard surface of the original manifold. We show that any two Heegaard surfaces in different fillings, into which the core is not isotopic, can be isotoped to intersect essentially. Using this, a bound on the distance between fillings containing such surfaces is given in terms of the genera of the Heegaard surfaces.