Algorithmic Topology and Classification of 3-ManifoldsFrom 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 monograph... All 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 für Mathematik 2004 For 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. |
Contents
1 | |
Complexity Theory of 3Manifolds | 59 |
Haken Theory of Normal Surfaces | 107 |
Applications of the Theory of Normal Surfaces 147 | 146 |
Algorithmic Recognition of S3 | 191 |
Classification of Haken 3Manifolds | 213 |
The TuraevViro Invariants | 383 |
of TuraevViro Type | 409 |
A Appendix | 421 |
References 481 | 480 |
Index | 489 |