Grope Height Raising and 1-storey Capped Towers

P. Feller, Mark D. Powell, Arunima Ray
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Abstract

‘Grope Height Raising and 1-Storey Capped Towers’ upgrades the capped gropes constructed in the previous chapter to 1-storey capped towers. Grope height raising is a technique that shows that every capped grope of height at least 1.5 can be improved to a capped grope of arbitrary height. The technique is explained in this chapter in detail, and used multiple times in the rest of the proof. The chapter closes by showing how to extend capped gropes to 1-storey capped towers. This crucially uses the hypothesis that the fundamental group is good. It is the single place in the proof of the disc embedding theorem that requires this hypothesis.
探索高度提升和1层封顶塔
“Grope Height Raising and 1-Storey Capped Towers”将前一章建造的封顶Grope升级为1层封顶塔。攀爬高度提升是一种技术,表明每个高度至少为1.5的攀爬都可以改进为任意高度的攀爬。该技术将在本章中详细解释,并在证明的其余部分中多次使用。本章最后展示了如何将封顶的地块扩展到1层封顶的塔楼。这很关键地利用了一个假设,即基本群是好的。在圆盘嵌入定理的证明中只有一个地方需要这个假设。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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