Intersection Numbers and the Statement of the Disc Embedding Theorem

Mark Powell, Arunima Ray
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引用次数: 1

Abstract

‘Intersection Numbers and the Statement of the Disc Embedding Theorem’ provides detailed definitions of some of the notions involved in the statement of the disc embedding theorem, focusing specifically on intersection numbers. The chapter begins with a detailed analysis of immersions, regular homotopies, finger moves, and Whitney moves. Then it defines intersection and self-intersection numbers for families of discs and spheres, taking values in the group ring of the fundamental group of the ambient space, with the correct relations. Then it enumerates certain properties of intersection numbers, in particular relating them to the existence of Whitney discs. This work enables the disc embedding theorem to be stated carefully.
交点数与圆盘嵌入定理的表述
“交点数与盘嵌入定理的表述”提供了盘嵌入定理表述中涉及的一些概念的详细定义,特别关注交点数。本章以详细分析浸入、正则同伦、手指移动和惠特尼移动开始。然后定义圆盘族和球族的交点数和自交点数,取周围空间基本群的群环上的值,并取正确的关系。然后列举了交数的某些性质,特别是与惠特尼盘的存在性的关系。这一工作使盘片嵌入定理得以仔细地表述。
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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