High-dimensional Knot Theory : Algebraic Surgery in Codimension 2

Andrew Ranicki

ISBN 10: 3540633898 / ISBN 13: 9783540633891

Editore: Springer, Springer Vieweg, 1998

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Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9783540633891

Dati bibliografici

• Titolo: High-dimensional Knot Theory : Algebraic Surgery in Codimension 2
• Editore: Springer, Springer Vieweg
• Data di pubblicazione: 1998
• Lingua: Inglese
• ISBN 10: 3540633898
• ISBN 13: 9783540633891
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 42 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 42 millimetri di profondità
• Peso: 1191 grammi

Descrizione articolo

Riassunto

Bringing together many results previously scattered throughout the research literature into a single framework, this work concentrates on 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.

Dalla quarta di copertina

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. This is the first book entirely devoted to high-dimensional knots. 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.