Algorithmic Topology and Classification of 3-Manifolds
By: by Sergei Matveev
Series: Algorithms and Computation in Mathematics -- 9; Algorithms and Computation in Mathematics -- 9
Publisher: Springer Berlin Heidelberg
Published: 2003
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 478
ISBN-13: 9783662051047; 9783662051023
Subjects: Algorithms; Data processing; Algebra; Global differential geometry; Mathematics; Topology
Description: This self-contained book by a leading topologist is devoted to algorithmic low-dimensional topology, a branch of mathematics that has recently been undergoing an intense development. The book contains plenty of important fundamental material, which is carefully presented. The book also contains some of the author's own original contributions. For the first time ever, it gives a full exposition of the complexity theory of 3-manifolds and a complete proof of the solution of the homeomorphism problem for Haken manifolds. The subject of the book is the topology of bare 3-manifolds, without geometric structures, which became incorporated into 3-dimensional topology by the work of Thurston. This non-geometric part of low-dimensional topology is presented by Matveev in a truly geometric way. Although the author emphasizes the algorithmic side of the subject, the book presents also the background non-algorithmic contents of the subject. The style of the book is very lively, with a lot of useful pictures, making the book enjoyable for those who like visual topology. The writing is clear and the proofs are careful and detailed. This book fills a gap in the exisiting literature and will become a standard reference for this aspect of 3-dimensional topology both for graduate students and researchers.
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Table of contents: title: Simple and special polyhedra; title: Complexity theory of 3-manifolds; title: Haken theory of normal surfaces; title: Applications of the theory of normal surfaces; title: Algorithmic recognition of S3; title: Classification of Haken 3-manifolds; title: Computer implementation; title: The Turaev-Viro invariants; title: Appendix.