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Algorithmic Topology and Classification of 3-Manifolds [electronic resource] /by Sergei Matveev.

by Matveev, Sergei [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Algorithms and Computation in Mathematics: 9Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.Description: XIV, 492 p. 264 illus. online resource.ISBN: 9783540458999.Subject(s): Mathematics | Algebra -- Data processing | Algorithms | Global differential geometry | Topology | Mathematics | Topology | Differential Geometry | Algorithms | Symbolic and Algebraic ManipulationDDC classification: 514 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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". R. Piergallini, Zentralblatt für Mathematik 1048 (2004) For this 2nd edition, new results, new proofs, and commentaries for a better orientation of the reader have been added.
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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.

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". R. Piergallini, Zentralblatt für Mathematik 1048 (2004) For this 2nd edition, new results, new proofs, and commentaries for a better orientation of the reader have been added.

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