Algorithmic Topology and Classification of 3-Manifolds

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Springer Science & Business Media, Jul 23, 2007 - Mathematics - 492 pages
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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 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.

 

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Contents

Simple and Special Polyhedra
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
A Appendix
421
References 481
480
Index
489
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