三維流形拓撲學講義(第2版英文) ,

作者:薩韋列夫,

出版社:世界圖書出版公司北京公司

ISBN:9787519219208

$20.75

產品號碼: 85753 貨號: 9787519219208 分類: , 標籤: , , ,

主要介紹低維拓撲和Casson理論,當然也不失適時地引入最近研究進展和課題。包括許多經典材料,如Heegaard分裂、Dehn手術、扭結和連接不變數。從Kirby微積分開始,進一步講述Rohlin定理,直到Casson不變數及其應用,並以簡短介紹最新進展作為結束。熟悉基礎代數和微分拓撲,包括基礎群、基本同調理論、橫截性和流形上的龐加萊對偶性的數學和理論物理專業的讀者均可閱讀。

目錄

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≤1
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 incersection 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 invariants 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—invarianc 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 coborclism 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 spaccs
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 Heegaard 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 Cassoninvariant for boundary links
175 The Casson invariant of a trefoil

18 An application of the Casson invariant
18.1 Triangulating 4—manifolds
18.2 Higher—dimcnsional 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

出版日期

01/01/2017

語系

簡體中文

版別

初版

裝訂

平裝

頁數

207

印刷

單色印刷

出版地

大陸