High-dimensional knot theory. Algebraic surgery in codimension 2. With errata
High-dimensional knot theory. Algebraic surgery in codimension 2. With errata By Andrew Ranicki, E. Winkelnkemper
1998 | 706 Pages | ISBN: 3540633898 | PDF | 3 MB
1998 | 706 Pages | ISBN: 3540633898 | PDF | 3 MB
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.