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Algorithmic Topology and Classification of 3-Manifolds

  • Sergei┬áMatveev

Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 9)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Sergei Matveev
    Pages 1-58
  3. Sergei Matveev
    Pages 59-106
  4. Sergei Matveev
    Pages 107-145
  5. Sergei Matveev
    Pages 147-191
  6. Sergei Matveev
    Pages 193-214
  7. Sergei Matveev
    Pages 215-328
  8. Sergei Matveev
    Pages 329-366
  9. Sergei Matveev
    Pages 367-403
  10. Sergei Matveev
    Pages 405-466
  11. Back Matter
    Pages 467-478

About this book

Introduction

This self-contained book by a leading topologist is devoted to algorithmic low-dimensional topology, a branch of mathematics that has recently been undergoing an intense development. The book contains plenty of important fundamental material, which is carefully presented. The book also contains some of the author's own original contributions. For the first time ever, it gives a full exposition of the complexity theory of 3-manifolds and a complete proof of the solution of the homeomorphism problem for Haken manifolds. The subject of the book is the topology of bare 3-manifolds, without geometric structures, which became incorporated into 3-dimensional topology by the work of Thurston. This non-geometric part of low-dimensional topology is presented by Matveev in a truly geometric way. Although the author emphasizes the algorithmic side of the subject, the book presents also the background non-algorithmic contents of the subject. The style of the book is very lively, with a lot of useful pictures, making the book enjoyable for those who like visual topology. The writing is clear and the proofs are careful and detailed. This book fills a gap in the exisiting literature and will become a standard reference for this aspect of 3-dimensional topology both for graduate students and researchers.

Keywords

3-manifold Homeomorphism algorithmic recognition algorithms ants classification complexity special spine sufficiently large manifold

Authors and affiliations

  • Sergei┬áMatveev
    • 1
  1. 1.Chelyabinsk State UniversityChelyabinskRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-05102-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-05104-7
  • Online ISBN 978-3-662-05102-3
  • Series Print ISSN 1431-1550
  • Buy this book on publisher's site