三维流形的α-倾斜广义Heegaard分裂
alpha-sloped Generalized Heegaard splittings of 3-manifolds
摘要：
推广了Scharlemann和Thompson关于具有环面边界分支的紧致可定向三维流形的薄位置的定义，并引入了$α$ -倾斜广义Heegaard分裂.我们研究它的关系，广义Heegaard分裂的流形Dehn填充。我们比较了3-流形的α-倾斜薄位置与其他类型的节点和3-流形的薄位置，并讨论了这种分解如何给出M的有机图像，并允许流形的结构决定边界上最自然的斜率。此外，我们提供了说明性的例子和问题，激励研究α倾斜薄的位置。
英文摘要：
We generalize the definition of thin position of Scharlemann and Thompson for compact orientable 3-manifolds with torus boundary components and introduce $α$-sloped generalized Heegaard splittings. We examine its relationship to generalized Heegaard splittings of manifolds resulting from Dehn filling. We compare alpha-sloped thin position of 3-manifolds to other types of thin position for knots and 3-manifolds and discuss how this kind of decomposition gives an organic picture of M and allows the structure of the manifold to dictate the most natural slope(s) on the boundary. Additionally, we provide illustrative examples and questions motivating the study of alpha-sloped thin position.
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