Algorithmic Topology and Classification of 3-Manifolds

• Κύριος συγγραφέας: Matveev, Sergei (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.
• Σειρά: Algorithms and Computation in Mathematics, 9
• Θέματα: Mathematics.; Computer programming.; Computer science > Mathematics.; Algorithms.; Differential geometry.; Topology.; Programming Techniques.; Differential Geometry.; Symbolic and Algebraic Manipulation.

 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. 

 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.