3 维流形引论（影印版）

样章

作者：

Jennifer Schultens

定价：

135.00 元

版面字数：

500千字

开本：

16开

装帧形式：

精装

版次：

最新版次
印刷时间：

2023年

ISBN：

978-7-04-059303-7

物料号：

59303-00

出版时间：

2023-03-24

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

代数几何学

暂无

目录
- 前辅文
- Chapter 1 Perspectives on Manifolds
  - 1.1 Topological Manifolds
  - 1.2 Differentiable Manifolds
  - 1.3 Oriented Manifolds
  - 1.4 Triangulated Manifolds
  - 1.5 Geometric Manifolds
  - 1.6 Connected Sums
  - 1.7 Equivalence of Categories
- Chapter 2 Surfaces
  - 2.1 A Few Facts about 1-Manifolds
  - 2.2 Classification of Surfaces
  - 2.3 Decompositions of Surfaces
  - 2.4 Covering Spaces and Branched Covering Spaces
  - 2.5 Homotopy and Isotopy on Surfaces
  - 2.6 The Mapping Class Group
- Chapter 3 3-Manifolds
  - 3.1 Bundles
  - 3.2 The Sch¨onflies Theorem
  - 3.3 3-Manifolds that are Prime but Reducible
  - 3.4 Incompressible Surfaces
  - 3.5 Dehn’s Lemma*
  - 3.6 Hierarchies*
  - 3.7 Seifert Fibered Spaces
  - 3.8 JSJ Decompositions
  - 3.9 Compendium of Standard Arguments
- Chapter 4 Knots and Links in 3-Manifolds
  - 4.1 Knots and Links
  - 4.2 Reidemeister Moves
  - 4.3 Basic Constructions
  - 4.4 Knot Invariants
  - 4.5 Zoology
  - 4.6 Braids
  - 4.7 The Alexander Polynomial
  - 4.8 Knots and Height Functions
  - 4.9 The Knot Group*
  - 4.10 Covering Spaces*
- Chapter 5 Triangulated 3-Manifolds
  - 5.1 Simplicial Complexes
  - 5.2 Normal Surfaces
  - 5.3 Diophantine Systems
  - 5.4 2-Spheres*
  - 5.5 Prime Decompositions
  - 5.6 Recognition Algorithms
  - 5.7 PL Minimal Surfaces**
- Chapter 6 Heegaard Splittings
  - 6.1 Handle Decompositions
  - 6.2 Heegaard Diagrams
  - 6.3 Reducibility and Stabilization
  - 6.4 Waldhausen’s Theorem
  - 6.5 Structural Theorems
  - 6.6 The Rubinstein-Scharlemann Graphic
  - 6.7 Weak Reducibility and Incompressible Surfaces
  - 6.8 Generalized Heegaard Splittings
  - 6.9 An Application
  - 6.10 Heegaard Genus and Rank of Fundamental Group*
- Chapter 7 Further Topics
  - 7.1 Basic Hyperbolic Geometry
  - 7.2 Hyperbolic n-Manifolds∗∗
  - 7.3 Dehn Surgery I
  - 7.4 Dehn Surgery II
  - 7.5 Foliations
  - 7.6 Laminations
  - 7.7 The Curve Complex
  - 7.8 Through the Looking Glass**
- Appendix A General Position
- Appendix B Morse Functions
- Bibliography
- Index