Skip to main content
SpringerLink
Log in
Book cover
  • Book
  • © 1998

High-dimensional Knot Theory

Algebraic Surgery in Codimension 2

Authors:

  1. Andrew Ranicki

    1. Department of Mathematics and Statistics, University of Edinburgh, Edinburgh, Scotland, UK

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Springer Monographs in Mathematics (SMM)

Sections

Buy it now

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, log in via an institution to check for access.

Table of contents (42 chapters)

  1. Front Matter

    Pages I-XXXVI
    PDF

  2. Algebraic K-theory

    1. Front Matter

      Pages 1-1
      PDF

    2. Finite structures

      • Andrew Ranicki
      Pages 3-10

    3. Geometric bands

      • Andrew Ranicki
      Pages 11-13

    4. Algebraic bands

      • Andrew Ranicki
      Pages 15-18

    5. Localization and completion in K-theory

      • Andrew Ranicki
      Pages 19-26

    6. K-theory of polynomial extensions

      • Andrew Ranicki
      Pages 27-40

    7. K-theory of formal power series

      • Andrew Ranicki
      Pages 41-46

    8. Algebraic transversality

      • Andrew Ranicki
      Pages 47-56

    9. Finite domination and Novikov homology

      • Andrew Ranicki
      Pages 57-70

    10. Noncommutative localization

      • Andrew Ranicki
      Pages 71-78

    11. Endomorphism K-theory

      • Andrew Ranicki
      Pages 79-96

    12. The characteristic polynomial

      • Andrew Ranicki
      Pages 97-104

    13. Primary K-theory

      • Andrew Ranicki
      Pages 105-118

    14. Automorphism K-theory

      • Andrew Ranicki
      Pages 119-134

    15. Witt vectors

      • Andrew Ranicki
      Pages 135-150

    16. The fibering obstruction

      • Andrew Ranicki
      Pages 151-158

    17. Reidemeister torsion

      • Andrew Ranicki
      Pages 159-164

    18. Alexander polynomials

      • Andrew Ranicki
      Pages 165-176

    19. K-theory of Dedekind rings

      • Andrew Ranicki
      Pages 177-184
Back to top

About this book

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.
Back to top

Keywords

Back to top

Authors and Affiliations

  • Department of Mathematics and Statistics, University of Edinburgh, Edinburgh, Scotland, UK

    Andrew Ranicki

Back to top

Bibliographic Information

  • Book Title: High-dimensional Knot Theory

  • Book Subtitle: Algebraic Surgery in Codimension 2

  • Authors: Andrew Ranicki

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-12011-8

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1998

  • Hardcover ISBN: 978-3-540-63389-1Published: 06 August 1998

  • Softcover ISBN: 978-3-642-08329-7Published: 15 December 2010

  • eBook ISBN: 978-3-662-12011-8Published: 17 April 2013

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XXXVI, 646

  • Topics: Algebraic Topology

Back to top

Publish with us

Policies and ethics

Back to top
Access via your institution

Buy it now

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Search

Navigation