算法拓扑学及三维流形的分类 : 第2版

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

《算法拓扑学及三维流形的分类》提供了一个全面、详细的3-维流形的分类并介绍了算法拓扑学，该书的作者也是这方面领域的专家。该书是springer的AlgorithmsandComputationinMathematics丛书的第九本。属于"反映学术前沿进展的优秀学术著作"这一类。

From the reviews of the 1st edition： "This book provides aComprehensive and detailed account of different topics in algorithmic3-dimensional topology， culminating with the recognition procedurefor Haken manifolds and including the up-to-date results in computerenumeration of 3-manifolds. Originating from lecture notes of variouscourses given by the author over a decade， the book is intended tocombine the pedagogical approach of a graduate textbook （withoutexercises） with the completeness and reliability of a researchmonograph.-. All the material， with few exceptions， is presented fromthe peculiar point of view of special polyhedra and special spinesof 3-manifolds. This choice contributes to keep the level of theexposition really elementary. In conclusion， the reviewer subscribesto the quotation from the back cover： "the book fills a gap in theexisting literature and will become a standard reference for algorithmic3-dimensional topology both for graduate students and researchers".R. Piergallini， ZentralblattfUr Mathematik 1048 （2004） For this 2ndedition， new results， new proofs， and commentaries for a betterorientation of the reader have been added.