继Mazur, Morse和Brown之后的舍恩菲斯定理

Stefan Behrens, Allison N. Miller, M. Nagel, P. Teichner
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引用次数: 0

摘要

《继Mazur、Morse和Brown之后的舍恩菲斯定理》提供了舍恩菲斯定理的两个证明。舍恩菲斯定理指出,(n - 1)球在n球中的每一个双圈嵌入都将n球分割成两个球。本章提供了两个证明。第一个是马祖尔和莫尔斯;它利用了一种无限的“骗局”和一种叫做推拉的经典技术。第二个证明是由布朗提出的,作为收缩或分解空间理论的介绍。后者是一个漂亮但过时的拓扑分支,可以用来产生流形之间的不可微同胚,特别是从流形到商空间。在圆盘嵌入定理的证明中,分解空间理论中的技术是必不可少的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Schoenflies Theorem after Mazur, Morse, and Brown
‘The Schoenflies Theorem after Mazur, Morse, and Brown’ provides two proofs of the Schoenflies theorem. The Schoenflies theorem states that every bicollared embedding of an (n – 1)-sphere in the n-sphere splits the n-sphere into two balls. This chapter provides two proofs. The first is due to Mazur and Morse; it utilizes an infinite ‘swindle’ and a classical technique called push-pull. The second proof, due to Brown, serves as an introduction to shrinking, or decomposition space theory. The latter is a beautiful, but outmoded, branch of topology that can be used to produce non-differentiable homeomorphisms between manifolds, especially from a manifold to a quotient space. Techniques from decomposition space theory are essential in the proof of the disc embedding theorem.
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