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High-dimensional Knot Theory

Algebraic Surgery in Codimension 2

  • Andrew Ranicki

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

Table of contents

  1. Front Matter
    Pages I-XXXVI
  2. Algebraic K-theory

    1. Front Matter
      Pages 1-1
    2. Andrew Ranicki
      Pages 3-10
    3. Andrew Ranicki
      Pages 11-13
    4. Andrew Ranicki
      Pages 15-18
    5. Andrew Ranicki
      Pages 19-26
    6. Andrew Ranicki
      Pages 27-40
    7. Andrew Ranicki
      Pages 41-46
    8. Andrew Ranicki
      Pages 47-56
    9. Andrew Ranicki
      Pages 57-70
    10. Andrew Ranicki
      Pages 71-78
    11. Andrew Ranicki
      Pages 79-96
    12. Andrew Ranicki
      Pages 97-104
    13. Andrew Ranicki
      Pages 105-118
    14. Andrew Ranicki
      Pages 119-134
    15. Andrew Ranicki
      Pages 135-150
    16. Andrew Ranicki
      Pages 151-158
    17. Andrew Ranicki
      Pages 159-164
    18. Andrew Ranicki
      Pages 165-176
    19. Andrew Ranicki
      Pages 177-184
    20. Andrew Ranicki
      Pages 185-202
  3. Algebraic L-theory

    1. Front Matter
      Pages 203-203
    2. Andrew Ranicki
      Pages 205-224
    3. Andrew Ranicki
      Pages 225-231
    4. Andrew Ranicki
      Pages 233-256
    5. Andrew Ranicki
      Pages 261-266
    6. Andrew Ranicki
      Pages 267-286
    7. Andrew Ranicki
      Pages 287-301
    8. Andrew Ranicki
      Pages 303-320
    9. Andrew Ranicki
      Pages 321-350
    10. Andrew Ranicki
      Pages 351-368
    11. Andrew Ranicki
      Pages 369-396
    12. Andrew Ranicki
      Pages 397-414
    13. Andrew Ranicki
      Pages 415-442
    14. Andrew Ranicki
      Pages 443-452
    15. Andrew Ranicki
      Pages 453-465
    16. Andrew Ranicki
      Pages 467-484
    17. Andrew Ranicki
      Pages 485-489
    18. Andrew Ranicki
      Pages 491-498
    19. Andrew Ranicki
      Pages 499-510
    20. Andrew Ranicki
      Pages 511-559
    21. Andrew Ranicki
      Pages 561-582
    22. Andrew Ranicki
      Pages 583-605
    23. Andrew Ranicki
      Pages 607-612
  4. Back Matter
    Pages 613-646

About this book

Introduction

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. This is the first book entirely devoted to high-dimensional knots. 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.

Keywords

K-theory homology knots manifolds open books surgery

Authors and affiliations

  • Andrew Ranicki
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of EdinburghEdinburghScotland, UK

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-12011-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08329-7
  • Online ISBN 978-3-662-12011-8
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site