High-Dimensional Knot Theory: Algebraic Surgery in Codimension 2 (Hardcover) (ISBN-13: 9783540633891)

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.

Author: E. Winkelnkemper, Andrew Ranicki
ISBN-10: 3540633898
ISBN-13: 9783540633891
Publisher: Springer
Language: English
Published: 08/06/1998
Pages: 646
Format: Hardcover
Weight: 2.20lbs
Size: 9.52h x 6.39w x 1.58d