Sergei Matveev (auth.)3540458980, 978-3-540-45898-2
From the reviews of the 1st edition:”This book provides a comprehensive and detailed account of different topics in algorithmic 3-dimensional topology, culminating with the recognition procedure for Haken manifolds and including the up-to-date results in computer enumeration of 3-manifolds. Originating from lecture notes of various courses given by the author over a decade, the book is intended to combine the pedagogical approach of a graduate textbook (without exercises) with the completeness and reliability of a research monographAll the material, with few exceptions, is presented from the peculiar point of view of special polyhedra and special spines of 3-manifolds. This choice contributes to keep the level of the exposition really elementary.In conclusion, the reviewer subscribes to the quotation from the back cover: “the book fills a gap in the existing literature and will become a standard reference for algorithmic 3-dimensional topology both for graduate students and researchers’.Zentralblatt fur Mathematik 2004For this 2nd edition, new results, new proofs, and commentaries for a better orientation of the reader have been added. In particular, in Chapter 7 several new sections concerning applications of the computer program “3-Manifold Recognizer” have been included. |
Table of contents :
Front Matter….Pages I-XII
Simple and Special Polyhedra….Pages 1-58
Complexity Theory of 3-Manifolds….Pages 59-106
Haken Theory of Normal Surfaces….Pages 107-145
Applications of the Theory of Normal Surfaces….Pages 147-191
Algorithmic Recognition of S 3 ….Pages 193-214
Classification of Haken 3-Manifolds….Pages 215-328
Computer Implementation….Pages 329-366
The Turaev-Viro Invariants….Pages 367-403
Appendix….Pages 405-466
Back Matter….Pages 467-478 |
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