High-dimensional Knot Theory

Andrew Ranicki

ISBN 10: 3540633898 / ISBN 13: 9783540633891

Edité par Springer Berlin Heidelberg, Springer Berlin Heidelberg Aug 1998, 1998

A propos de cet article

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 692 pp. Englisch.

N° de réf. du vendeur 9783540633891

Détails bibliographiques

• Titre: High-dimensional Knot Theory
• Éditeur: Springer Berlin Heidelberg, Springer Berlin Heidelberg Aug 1998
• Date de parution: 1998
• Langue: anglais
• ISBN à 10 chiffres: 3540633898
• ISBN à 13 chiffres: 9783540633891
• Reliure: Buch
• État de l'article: Neu

A propos de ce titre

Synopsis

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.

Présentation de l'éditeur

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.