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Other titles in the Algorithms and Computation in Mathematics series:
Algorithms and Computation in Mathematics, #9: Algorithmic Topology and Classification of 3-Manifoldsby Sergei Matveev
Synopses & Reviews
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, and also 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. Written in a clear and succinct manner the book adopts a lively style, with a lot of useful pictures, making it enjoyable for those who like visual topology. The proofs are careful and detailed. This 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.
Includes bibliographical references (p. -473) and index.
Table of 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.- Computer implementation.- The Turaev-Viro invariants.- Appendix.
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