算法拓扑学及三维流形的分类 英文影印版 第二版
出版时间： 2011年版
内容简介
　　From the reviews of the 1st edition： \Thisbook provides a comprehensive and detailed account of differenttopics in algorithmic 3-dimensional topology， culminating with therecognition procedure for Haken manifolds and including theup-to-date results in computer enumeration of 3-manifolds.Originating from lecture notes of various courses given by theauthor over a decade， the book is intended to combine thepedagogical 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 thepeculiar point of view of special polyhedra and special spines of3-manifolds. This choice contributes to keep the level of theexposition really elementary. In conclusion， the reviewersubscribes to the quotation from the back cover： \the book fills agap in the existing literature and will become a standard referencefor algorithmic 3-dimensional topology both for graduate studentsand researchers\.R. Piergallini， Zentralblattfilr Mathematik 1048（2004） For this 2nd edition， new results， new proofs， andcommentaries for a better orientation of the reader have beenadded.
目录
Simple and Special Polyhedra
1.1　Spines of 3-Manifolds
1.1.1　Collapsing
1.1.2　Spines
1.1.3　Simple and Special Polyhedra
1.1.4　Special Spines
1.1.5　Special Polyhedra and Singular Triangulations
1.2　Elementary Moves on Special Spines　~
1.2.1　Moves on Simple Polyhedra
1.2.2　2-Cell Replacement Lemma
1.2.3　Bubble Move
1.2.4　Marked Polyhedra
1.3　Special Polyhedra Which are not Spines
1.3.1　Various Notions of Equivalence for Polyhedra
1.3.2　Moves on Abstract Simple Polyhedra
1.3.3　How to Hit the Target Without Inverse U-Turns
1.3.4　Zeeman's Collapsing Conjecture
Complexity Theory of 3-Manifolds
2.1　What is the Complexity of a 3-Manifold?
2.1.1　Almost Simple Polyhedra
2.1.2　Definition and Estimation of the Complexity
2.2　Properties of Complexity
2.2.1　Converting Almost Simple Spines into Special Ones..
2.2.2　The Finiteness Property
2.2.3　The Additivity Property
2.3　Closed Manifolds of Small Complexity
2.3.1　Enumeration Procedure
2.3.2　Simplification Moves
2.3.3　Manifolds of Complexity < 6
Contents
2.4　Graph Manifolds of Waldhausen
2.4.1　Properties of Graph Manifolds
2.4.2　Manifolds of Complexity <_8
2.5　Hyperbolic Manifolds
2.5.1　Hyperbolic Manifolds of Complexity 9
2.6　Lower Bounds of the Complexity
2.6.1　Logarithmic Estimates
2.6.2　Complexity of Hyperbolic 3-Manifolds
2.6.3　Manifolds Having Special Spines with One 2-Cell
Haken Theory of Normal Surfaces
3.1　Basic Notions and Haken's Scheme
3.2　Theory of Normal Curves
3.2.1　Normal Curves and Normal Equations
3.2.2　Fundamental Solutions and Fundamental Curves
3.2.3　Geometric Summation
3.2.4　An Alternative Approach to the Theory of Normal
Curves
3.3　Normal Surfaces in 3-Manifolds
3.3.1　Incompressible Surfaces
3.3.2　Normal Surfaces in 3-Manifolds with Boundary Pattern
3.3.3　Normalization Procedure
3.3.4　Fundamental Surfaces
3.3.5　Geometric Summation
3.4　Normal Surfaces in Handle Decompositions
4　 Applications of the Theory of Normal Surfaces
4.1　Examples of Algorithms Based on Haken's Theory
4.1.1　Recognition of Splittable Links
4.1.2　Getting Rid of Clean Disc Patches
4.1.3　Recognizing the Unknot and Calculating the Genus
of a Circle in the Boundary of a 3-Manifold
4.1.4　Is M3 Irreducible and Boundary Irreducible?
4.1.5　Is a Proper Surface Incompressible and Boundary
Incompressible?
4.1.6　Is M3 Sufficiently Large?
4.2　Cutting 3-Manifolds along Surfaces
4.2.1　Normal Surfaces and Spines
4.2.2　Triangulations vs. Handle Decompositions
5　 Algorithmic Recognition of Sa
5.1　Links in a 3-Ball
5.1.1　Compressing Discs and One-legged Crowns
5.1.2　Thin Position of Links
……
6　Classiflcation of Haken 3-Manifolds
7　3-Manifold Recognizer