High-dimensional Knot Theory

Algebraic Surgery in Codimension 2

von Andrew Ranicki

646 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Reihe: Springer Monographs in Mathematics
• ISBN: 9783642083297
• Sprache: Englisch
• Erscheinungsdatum: 15.12.2010
• Genre: Mathematik/Geometrie
• Verlag: Springer Berlin
• Anhang von: E. Winkelnkemper