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

Andrew Ranicki (Author), E. Winkelnkemper (Contributor)

Book Description

Publication Date: September 18, 1998 | ISBN-10: 3540633898 | ISBN-13: 978-3540633891 | Edition: 1

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.

Editorial Reviews

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.

Product Details

• Hardcover: 682 pages
• Publisher: Springer; 1 edition (September 18, 1998)
• Language: English
• ISBN-10: 3540633898
• ISBN-13: 978-3540633891
• Product Dimensions: 9.5 x 6.4 x 1.6 inches
• Shipping Weight: 2.2 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #3,560,663 in Books (See Top 100 in Books)

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