High-dimensional knot theory
High-dimensional knot theory
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高维纽结理论
DOI：
10.1007/978-3-662-12011-8
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发表时间：
1998
影响因子：
0.9
通讯作者：
A. Ranicki
中科院分区：
文献类型：
--
作者：
A. Ranicki
高维结理论是研究n维流形在(n+2)维流形中的嵌入，概括了n=1情况下结的传统研究。主题是应用作者的外科代数理论对余维2嵌入的不变量提供统一的处理，推广了经典结的亚历山大多项式和Seifert形式 理论。研究文献中的许多结果因此被纳入一个单一的框架中，并获得新的结果。该处理在处理开放书时特别有效，开放书是具有余维 2 子流形的流形，使得补纤维位于一个圆上。本书最后附有 E. Winkelnkemper 撰写的关于开放书籍历史的附录。
High-dimensional knot theory is the study of the embeddings of n-dimensional manifolds in (n+ 2)-dimensional manifolds, generalizing the traditional study of knots in the case n= 1. The main theme is the application of the author's algebraic theory of surgery to provide a unified treatment of the invariants of codimension 2 embeddings, generalizing the Alexander polynomials and Seifert forms of classical knot theory. Many results in the research literature are thus brought into a single framework, and new results are obtained. The treatment is particularly effective in dealing with open books, which are manifolds with codimension 2 submanifolds such that the complement fibres over a circle. The book concludes with an appendix by E. Winkelnkemper on the history of open books.