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Algorithms and Computation in Mathematics #9: Algorithmic Topology and Classification of 3-Manifolds

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Algorithms and Computation in Mathematics #9: Algorithmic Topology and Classification of 3-Manifolds Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

Reviews of the first edition of this book describe it as "a standard reference for algorithmic 3-dimensional topology both for graduate students and researchers". The 2nd edition adds new results, new proofs and commentaries for the benefit of the reader.

Table of Contents

1 Simple and Special Polyhedra.- 2 Complexity Theory of 3-Manifolds.- 3 Haken Theory of Normal Surfaces.- 4 Applications of the Theory of Normal Surfaces.- 5 Algorithmic Recognition of $S^3$.- 6 Classification of Haken 3-Manifolds.- 7 3-Manifold Recognizer.- 8 The Turaev-Viro Invariants.- Appendix.- 9.1 Manifolds of Complexity $\leq 6.- 9.2 Minimal Spines of Manifolds up to Complexity 6.- 9.3 Minimal Spines of Some Manifolds of Complexity 7.- 9.4 Tables of Turaev-Viro Invariants.- References.- Index

Product Details

ISBN:
9783540458982
Author:
Matveev, Sergei
Publisher:
Springer
Subject:
Topology - General
Subject:
Applied
Subject:
Topology
Subject:
3-manifold
Subject:
algorithmic recognition
Subject:
special spine
Subject:
sufficiently large manifold
Subject:
Differential geometry
Subject:
Algorithms
Subject:
Symbolic and Algebraic Manipulation
Subject:
MATHEMATICS / Topology
Copyright:
Edition Number:
2
Edition Description:
2nd ed. 2007
Series:
Algorithms and Computation in Mathematics
Series Volume:
9
Publication Date:
20070914
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
506
Dimensions:
235 x 155 mm

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Algorithms and Computation in Mathematics #9: Algorithmic Topology and Classification of 3-Manifolds New Hardcover
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Product details 506 pages Springer - English 9783540458982 Reviews:
"Synopsis" by , Reviews of the first edition of this book describe it as "a standard reference for algorithmic 3-dimensional topology both for graduate students and researchers". The 2nd edition adds new results, new proofs and commentaries for the benefit of the reader.
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