内容简介

目录

作　者：（俄）马特维耶夫 编著

出 版 社：科学出版社

出版时间：2011-6-1

页　数：492

字　数：630000

印刷时间：2011-6-1

开　本：16开

内容简介

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, Zentralblattfilr Mathematik 1048 (2004) For this 2nd edition, new results, new proofs, and commentaries for a better orientation of the reader have been added.

目录

1 simple and special polyhedra

1.1 spines of 3-manifolds

1.2 elementary moves on special spines

1.3 special polyhedra which are not spines

2 complexity theory of 3-manifolds

2.1what is the complexity of a 3-manifold?

2.2properties of complexity

2.3closed manifolds of small complexity

2.4graph manifolds of waldhausen

2.5hyperbolic manifolds

2.6lower bounds of the complexity

3 haken theory of normal surfaces

3.1 basic notions and haken's scheme

3.2 theory of normal curves

3.3 normal surfaces in 3-manifolds

3.4 normal surfaces in handle decompositions

4 applications of the theory of normal surfaces

6 Classification of Haken 3-Manifolds

5 algorithmic recognition of sa

7 3-manifold recognizer

8 the turaev-viro invariants

references

index