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

Book 4 of 187: Springer Monographs in Mathematics

Ranicki, Andrew

 
9783540633891: High-dimensional Knot Theory: Algebraic Surgery in Codimension 2 (Springer Monographs in Mathematics)
Hardcover
ISBN 10: 3540633898 ISBN 13: 9783540633891
Publisher: Springer, 1998

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.

"synopsis" may belong to another edition of this title.

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.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
1998
Language
English
ISBN 10 
3540633898
ISBN 13 
9783540633891
Binding
Hardcover
Number of pages
682

Other Popular Editions of the Same Title

9783642083297: High-dimensional Knot Theory: Algebraic Surgery in Codimension 2 (Springer Monographs in Mathematics)

Featured Edition

ISBN 10:  3642083293 ISBN 13:  9783642083297
Publisher: Springer, 2010
Softcover