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High-dimensional Knot Theory

Algebraic Surgery in Codimension 2

Andrew Ranicki

Editore:: Springer Berlin Heidelberg
Collana:: Springer Monographs In Mathematics
EAN:: 9783540633891
ISBN:: 3540633898
Pagine:: 692
Formato:: Hardback
Lingua:: Tedesco

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Descrizione 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.

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High-dimensional Knot Theory

Algebraic Surgery in Codimension 2

Andrew Ranicki

Springer Berlin Heidelberg

9783540633891

3540633898

Descrizione High-dimensional Knot Theory

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