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High-dimensional Knot Theory
Andrew Ranicki
其他書名
Algebraic Surgery in Codimension 2
出版Springer Science & Business Media, 2013-04-17
主題Mathematics / TopologyMathematics / Geometry / General
ISBN36621201199783662120118
URLhttp://books.google.com.hk/books?id=nCvrCAAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋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.