High-dimensional Knot Theory
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.
| Autor: | Ranicki, Andrew |
|---|---|
| ISBN: | 9783540633891 |
| Sprache: | Englisch |
| Seitenzahl: | 646 |
| Produktart: | Gebunden |
| Verlag: | Springer Berlin |
| Veröffentlicht: | 06.08.1998 |
| Untertitel: | Algebraic Surgery in Codimension 2 |
| Schlagworte: | K-theory homology knots manifolds open books surgery |