Waldhausen's Theorem
Waldhausen's Theorem
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瓦尔德豪森定理
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
S. Schleimer
中科院分区：
文献类型：
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作者：
S. Schleimer
瓦尔德豪森定理（Waldhausen’s Theorem）告诉我们，三球的分裂是唯一的，直到同位素。这是低维拓扑中的一个重要工具，并且有几个现代证明（Jaco和Rubinstein [16]， Rieck [28] Rubinstein和Scharlemann[31]和Scharlemann和Thompson[33]）。此外，至少有两篇关于Heegaard分裂的综述文章（Johnson b[17]和Scharlemann[32]）包括了瓦尔德豪森定理的证明。这个说明是为了说明瓦尔德豪森的原始证明，因为他的技术仍然感兴趣。例如，Bartolini和Rubinstein对RP的片面分裂的[3]分类
Waldhausen’s Theorem [36] tells us that Heegaard splittings of the three-sphere areunique up to isotopy. This is an important tool in low-dimensional topology andthere are several modern proofs (Jaco and Rubinstein [16], Rieck [28] Rubinstein andScharlemann [31] and Scharlemann and Thompson [33]). Additionally, at least twosurvey articles on Heegaard splittings (Johnson [17] and Scharlemann [32]) includeproofs of Waldhausen’s Theorem.This note is intended as an exposition of Waldhausen’s original proof, as his techniquesare still of interest. See, for example, Bartolini and Rubinstein’s [3] classification ofone-sided splittings of RP