软木扭转Schoenflies问题
Cork twisting Schoenflies problem
摘要：
组合群论中的稳定Andrews-Curtis猜想是这样的陈述：平凡群的每个平衡表示都可以通过对应于“滑动”的基本移动和“稳定化”移动简化为平凡形式。Schoenflies猜想是关于任意光滑嵌入S^3到S^4的补是一对光滑球的命题。本文提出了在可收缩流形上通过某种cork扭曲操作来解决这些问题的方法，并以第一Cappell-Shaneson同伦球面为例加以证明.
英文摘要：
The stable Andrews-Curtis conjecture in combinatorial group theory is the statement that every balanced presentation of the trivial group can be simplified to the trivial form by elementary moves corresponding to "handle-slides" together with "stabilization" moves. Schoenflies conjecture is the statement that the complement of any smooth embedding S^3 into S^4 are pair of smooth balls. Here we suggest an approach to these problems by certain cork twisting operation on contractible manifolds, and demonstrate it on the example of the first Cappell-Shaneson homotopy sphere.
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