3-阶Poincare猜想的Heegaard分裂初等证明
An Elementary Proof by the Heegaard Splittings of the 3-Dimentional Poincare Conjecture
摘要：
v1：本文从PL拓扑的观点出发，利用Heegaard分裂给出了三维Poincare猜想的一个初等证明。本文与文[4]（1983）的理论相同，但不包括主要定理的最后三行证明。v2：本文给出了[1]（1997）的基本结果，即，Heegaard图的柄滑动和带移动分别对应于由Heegaard图导出的基本群的关系中的替换和代换（定理12）。推论13是同伦3-球面的一个新的补充。
英文摘要：
v1: In this paper, we will give an elementary proof by the Heegaard splittings of the 3-dimentional Poincare conjecture in point of view of PL topology. This paper is of the same theory in [4](1983) excluding the last three lines of the proof of the main theorem. v2: This paper gives the basic result of [1](1997), i.e., a handle sliding and a band move of Heegaard diagrams correspond to a replacement and a substitution in relations of the fundamental groups derived from Heegaard diagrams, respectively (Theorem 12). Corollary 13 is a new addition for the homotopy 3-sphere.
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