Springer Monographs in Mathematics: Algebraic Surgery in Codimension 2

Winkelnkemper, E.; Ranicki, Andrew

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.

Details

Published by: Springer

Publication Date: 1998-08-06

Format: Hardcover

ISBN-13: 9783540633891

DOI: 10.1007/978-3-662-12011-8

Dimensions: 235cm x155cm

Pages: 646