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.
| Autorius: | Andrew Ranicki |
| Serija: | Springer Monographs in Mathematics |
| Leidėjas: | Springer Berlin Heidelberg |
| Išleidimo metai: | 2010 |
| Knygos puslapių skaičius: | 688 |
| ISBN-10: | 3642083293 |
| ISBN-13: | 9783642083297 |
| Formatas: | Knyga minkštu viršeliu |
| Kalba: | Anglų |
| Žanras: | Algebraic topology |
Parašykite atsiliepimą apie „High-dimensional Knot Theory: Algebraic Surgery in Codimension 2“
