4維流形與Kirby演算(英文版)(精)/美國數學會經典影印系列
內容大鋼
過去的二十年間，四維流形理論經歷了爆炸性增長。目前有許多書籍從規範理論或代數幾何等不同角度來探討這一主題。然而，本書提供了一種從拓撲學角度來闡述的方法。它彌合了與其他學科之間的鴻溝，並介紹了經典但重要的拓撲技術，這些技術以前在文獻中並未出現過。
本書的第一部分以研究生二年級水平介紹了該理論的基礎知識，並概述了當前的研究動向。第二部分專門講述了Kirby演算，即四維流形上的手柄體理論。這部分內容既基礎又全面。
第三部分深入探討了當前四維流形研究的廣泛課題。其中包括分支覆蓋和複雜曲面地理學、橢圓和Lefschetz纖維化、h-可邊界、辛四維流形和Stein曲面等課題。書中還提供了應用示例，配有300多幅插圖和大量習題及解答。
本書以拓撲學的觀點展開，向讀者介紹了該領域的經典技術，並涵蓋了相關研究的最新進展。它對於研究人員和學生們深入理解四維流形理論以及在其他學科中的應用具有重要意義。
作者介紹
(美)羅伯特·E.岡夫//(匈)安德拉斯·I.什蒂普希茨|責編:和靜
目錄
Preface
Part 1.4-Manifolds
Chapter 1.Introduction
1.1 .Manifolds
1.2 .4-manifolds
1.3 .Examples
1.4 .Appendix
Chapter 2.Surfaces in 4-manifolds
2.1 .Surfaces in CP2
2.2 .The blow-up process
2.3 .Desingularization of curves
2.4 .Appendix: Introduction to gauge theory
Chapter 3.Complex surfaces
3.1 .E(1) and fiber sum
3.2 .Other constructions of elliptic fbrationso rgolaqo
3.3 .Logarithmic transformation
3.4 .Classification of complex surfaces
Part 2.Kirby Calculus
Chapter 4.Handlebodies and Kirby diagrams
4.1 .Handles
4.2 .Handle decompositions
4.3 .Dimension three -Heegaard splittings
4.4 .Dimension four -Kirby diagrams
4.5 .Linking numbers and framings
4.6 .Examples
Chapter 5.Kirby calculus
5.1 .Handle moves
5.2 .Surgery
5.3 .Dehn surgery
5.4 .1-handles revisited
5.5 .Relative Kirby calculus
5.6 .Spin structures
5.7 .Spin structures in Kirby diagrams
Chapter 6.More examples
6.1 .Plumbings and related constructions
6.2 .Embedded surfaces and their complements
6.3 .Branched covers
Part 3.Applications
Chapter 7.Branched covers and resolutions
7.1 .Definitions and examples
7.2 .Resolution of singularities
7.3 .Elliptic surfaces revisited
7.4 .Surfaces of general type
Chapter 8.Elliptic and Lefschetz fibrations
8.1 .Lefschetz pencils and fibrations
8.2 .The topology of Lefschetz fibrations
8.3 .The topology of elliptic surfaces
8.4 .Higher genus and generalized fibrations
8.5 .Rationally blowing down
Chapter 9.Cobordisms, h-cobordisms and exotic R4's
9.1 .Cobordism groups
9.2 .h-cobordisms
9.3 .Akbulut corks and exotic R4's
9.4 .More exotica
Chapter 10.Symplectic 4-manifolds
10.1 .Symplectic and almost-complex manifolds
10.2 .Constructions of symplectic manifolds
10.3 .4-manifolds with no symplectic structure
10.4 .Gauge theory on symplectic 4-manifolds
Chapter 11.Stein surfaces
11.1 .Contact structures
11.2 .Kirby diagrams of Stein surfaces
11.3 .Invariants of Stein and contact structures
11.4 .Stein surfaces and gauge theory
Part 4.Appendices<
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