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Algorithmic and Computer Methods for Three-Manifolds

  • Book
  • © 1997

Overview

Authors:
  1. A. T. Fomenko

    1. Moscow State University, Moscow, Russia

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  2. S. V. Matveev

    1. Chelyabinsk State University, Chelyabinsk, Russia

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Mathematics and Its Applications (MAIA, volume 425)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Preliminary Information

    • A. T. Fomenko, S. V. Matveev
    Pages 1-31

  3. Surfaces

    • A. T. Fomenko, S. V. Matveev
    Pages 33-70

  4. The Homeotopy Group of a Surface

    • A. T. Fomenko, S. V. Matveev
    Pages 71-108

  5. The Presentation of Three-Dimensional Manifolds by the Identification of Faces of Polyhedra

    • A. T. Fomenko, S. V. Matveev
    Pages 109-122

  6. Heegaard Splittings and Heegaard Diagrams

    • A. T. Fomenko, S. V. Matveev
    Pages 123-144

  7. Algorithmic Recognition of the Sphere

    • A. T. Fomenko, S. V. Matveev
    Pages 145-157

  8. Connected Sums

    • A. T. Fomenko, S. V. Matveev
    Pages 159-177

  9. Knots and Links

    • A. T. Fomenko, S. V. Matveev
    Pages 179-205

  10. Surgery along Links

    • A. T. Fomenko, S. V. Matveev
    Pages 207-228

  11. Seifert Manifolds

    • A. T. Fomenko, S. V. Matveev
    Pages 229-270

  12. Class ℋ

    • A. T. Fomenko, S. V. Matveev
    Pages 271-286

  13. The Haken Method

    • A. T. Fomenko, S. V. Matveev
    Pages 287-297

  14. Back Matter

    Pages 299-337
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About this book

One service mathematics has rendered the human race. It has put common sense back where it belongs. It has put common sense back where it belongs, on the topmost shelf next to the dusty canister labelled discarded nonsense. Eric TBell Every picture tells a story. Advenisement for for Sloan's backache and kidney oils, 1907 The book you have in your hands as you are reading this, is a text on3-dimensional topology. It can serve as a pretty comprehensive text book on the subject. On the other hand, it frequently gets to the frontiers of current research in the topic. If pressed, I would initially classify it as a monograph, but, thanks to the over three hundred illustrations of the geometrical ideas involved, as a rather accessible one, and hence suitable for advanced classes. The style is somewhat informal; more or less like orally presented lectures, and the illustrations more than make up for all the visual aids and handwaving one has at one's command during an actual presentation.

Reviews

`I really enjoyed this book; it is great fun and full of enthusiasm for the subject. ... Furthermore, there are some excellent figures, which bring the book to life and often show really clearly what is going on.'
Bulletin of the London Mathematical Society, 32 (2000)
`This book is an attractive and comprehensive introduction to three-dimensional topology. The book is readable and inviting. Its many illustrations make it particularly accessible. This book promises to be a valuable text and reference for an exciting area of mathematics.'
SIAM Review, 41:2 (1999)

Authors and Affiliations

  • Moscow State University, Moscow, Russia

    A. T. Fomenko

  • Chelyabinsk State University, Chelyabinsk, Russia

    S. V. Matveev

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