Algorithmic Topology and Classification of 3-Manifolds

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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.


Simple and Special Polyhedra.- Complexity Theory of 3-Manifolds.- Haken Theory of Normal Surfaces.- Applications of the Theory of Normal Surfaces.- Algorithmic Recognition of S3.- Classification of Haken 3-Manifolds.- 3-Manifold Recognizer.- The Turaev-Viro Invariants.

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Algorithmic Topology and Classification of 3-Manifolds
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Springer Berlin Heidelberg
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