High-Dimensional Knot Theory Algebraic Surgery in Codimension 2 |
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| Appendix by:
| Winkelnkemper, E. |
| Author:
| Ranicki, Andrew |
| Series title: | Springer Monographs in Mathematics Ser. |
| ISBN: | 978-3-642-08329-7 |
| Publication Date: | Dec 2010 |
| Publisher: | Springer Berlin / Heidelberg
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| Imprint: | Springer |
| Book Format: | Paperback |
| List Price: | USD $109.99 |
Book Description:
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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...
More DescriptionHigh-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.