High-dimensional Knot Theory: Algebraic Surgery in Codimension 2 (Springer Monographs in Mathematics)

Ranicki, Andrew

ISBN 10: 3540633898 / ISBN 13: 9783540633891

Published by Springer, 1998

About this Item

In.

Seller Inventory # ria9783540633891_new

Bibliographic Details

• Title: High-dimensional Knot Theory: Algebraic Surgery in Codimension 2 (Springer Monographs in Mathematics)
• Publisher: Springer
• Publication Date: 1998
• Language: English
• ISBN 10: 3540633898
• ISBN 13: 9783540633891
• Binding: Hardcover
• Condition: New

About this title

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.

From the Back Cover

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.