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High-dimensional Knot Theory - Andrew Ranicki - Bog

Bag om High-dimensional Knot Theory

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.

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  • Sprog:
  • Engelsk
  • ISBN:
  • 9783642083297
  • Indbinding:
  • Paperback
  • Sideantal:
  • 688
  • Udgivet:
  • 15. December 2010
  • Størrelse:
  • 155x37x235 mm.
  • Vægt:
  • 1025 g.
  • 2-3 uger.
  • 2. Juli 2024
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Beskrivelse af High-dimensional Knot Theory

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.

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