- 三维流形拓扑学讲义(第2版)(英文版)
- - 作者：(美)萨韦列夫
  - 出版社：世界图书出版公司
  - ISBN：9787519219208
  - 出版日期：2017/01/01
  - 页数：224
- 售价：19.6

内容大纲
萨韦列夫著的《三维流形拓扑学讲义（第2版）（英文版）》主要介绍低维拓扑和Casson理论，当然也不失适时地引入最近研究进展和课题。包括许多经典材料，如Heegaard分裂、Dehn手术、扭结和连接不变量。从Kirby微积分开始，进一步讲述Rohlin定理，直到Casson不变量及其应用，并以简短介绍最新进展作为结束。熟悉基础代数和微分拓扑，包括基础群、基本同调理论、横截性和流形上的庞加莱对偶性的数学和理论物理专业的读者均可阅读。
作者介绍
目录
Preface
Introduction
Glossary
1  Heegaard splittings
  1.1  Introduction
  1.2  Existence of Heegaard splittings
  1.3  Stable equivalence of Heegaard splittings
  1.4  The mapping class group
  1.5  Manifolds of Heegaard genus _< I
  1.6  Seifert manifolds
  1.7  Heegaard diagrams
  1.8  Exercises
2  Dehn surgery
  2.1  Knots and links in 3-manifolds
  2.2  Surgery on links in S3
  2.3  Surgery description of lens spaces and Seifert manifolds
  2.4  Surgery and 4-manifolds
  2.5  Exercises
3  Kirby calculus
  3.1  The linking number
  3.2  Kirby moves
  3.3  The linking matrix
  3.4  Reversing orientation
  3.5  Exercises
4  Even surgeries
  4.1  Exercises
5  Review of 4-manifolds
  5.1  Definition of the intersection form
  5.2  The unimodular integral forms
  5.3  Four-manifolds and intersection forms
  5.4  Exercises
6  Four-manifolds with boundary
  6.1  The intersection form
  6.2  Homology spheres via surgery on knots
  6.3  Seifert homology spheres
  6.4  The Rohlin invariant
  6.5  Exercises
7  Invariants of knots and links
  7.1  Seifert surfaces
  7.2  Seifert matrices
  7.3  The Alexander polynomial
  7.4  Other i nvariants from Seifert surfaces
  7.5  Knots in homology spheres
  7.6  Boundary links and the Alexander polynomial
  7.7  Exercises
8  Fibered knots
  8.1  The definition of a fibered knot
  8.2  The monodromy
  8.3  More about torus knots
  8.4  Joins

  8.5  The monodromy of torus knots
  8.6  Open book decompositions
  8.7  Exercises
9  The Arf-invariant
  9.1  The Arf-invariant of a quadratic form
  9.2  The Arf-invariant of a knot
  9.3  Exercises
10 Rohlin's theorem
  10.1 Characteristic surfaces
  10.2 The definition of q
  10.3 Representing homology classes by surfaces
11 The Rohlin invariant
  11.1 Definition of the Rohlin invariant
  11.2 The Rohlin invariant of Seifert spheres
  11.3 A surgery formula for the Rohlin invariant
  11.4 The homology cobordism group
  11.5 Exercises
12 The Casson invariant
  12.1 Exercises
13 The group SU(2)
  13.1 Exercises
14 Representation spaces
  14.1 The topology of representation spaces
  14.2 Irreducible representations
  14.3 Representations of free groups
  14.4 Representations of surface groups
  14.5 Representations for Seifert homology spheres
  14.6 Exercises
15 The local properties of representation spaces
  15.1 Exercises
16 Casson's invariant for Heegaard splittings
  16.1 The intersection product
  16.2 The orientations
  16.3 Independence of l lcega~lvd splitting
  16.4 Exercises
17 Casson's invariant for knots
  17.1 Preferred Heegaard splittings
  17.2 The Casson invariant for knots
  17.3 The difference cycle
  17.4 The Casson invariant for boundary links
  17.5 The Casson invariant of a trefoil
18 An application of the Casson invariant
  18.1 Triangulating 4-manifolds
  18.2 Higher-dimensional manifolds
  18.3 Exercises
19 The Casson invariant of Seifert manifolds
  19.1 The space R(p,q, r)
  19.2 Calculation of the Casson invariant
  19.3 Exercises
Conclusion

Bibliography
Index

内容大纲

作者介绍

目录

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