定 價(jià)：199 元
叢書名：美國數(shù)學(xué)會(huì)經(jīng)典影印系列
- 作者：（美）利維烏·尼古拉耶斯庫（Liviu I. Nicolaescu）著
- 出版時(shí)間：2019/5/1
- ISBN：9787040469035
- 出 版 社：高等教育出版社
- 中圖法分類：O18
- 頁碼：484頁
- 紙張：膠版紙
- 版次：1
- 開本：16K
在本書中，作者通過大量例題，極為詳盡地講述了在獨(dú)立研究規(guī)范理論時(shí)所必需的一系列原理、技術(shù)和應(yīng)用，以及它在幾何和拓?fù)鋵W(xué)中的應(yīng)用。書中包括對(duì)大多數(shù)單連通代數(shù)曲面的 Seiberg-Witten不變量的完整且自足的計(jì)算，其中僅僅使用了 Witten 的分解法。書中還給出了剖分和粘貼 Seiberg-Witten不變量的一個(gè)新方法，并通過如下例子進(jìn)行講解：連通和定理，blow-up公式，以及對(duì)Fintushel和Stern的消滅結(jié)果的證明。本書適合用作微分幾何、代數(shù)拓?fù)洹⒒A(chǔ)偏微分方程和泛函分析的參考書。
Introduction
Chapter 1.Preliminaries
1.1.Bundles, connections and characteristic classes
1.1.1.Vector bundles and connections
1.1.2.Chern-Weil theory
1.2.Basic facts about elliptic equations
1.3.Clifford algebras and Dirac operators
1.3.1.Clifford algebras and their representations
1.3.2.The Spin and Spinc groups
1.3.3.Spin and spine structures
1.3.4.Dirac operators associated to spin and spinc structures
1.4.Complex differential geometry
1.4.1.Elementary complex differential geometry
1.4.2.Cauchy-Riemann operators
1.4.3.Dirac operators on almost Khler manifolds
1.5.Fredholm theory
1.5.1.Continuous families of elliptic operators
1.5.2 Genericity results
Chapter 2.The Seiberg-Witten Invariants
2.1.Seiberg-Witten monopoles
2.1.1.The Seiberg-Witten equations
2.1.2.The functional set-up
2.2.The structure of the Seiberg-Witten moduli spaces
2.2.1.The topology of the moduli spaces
2.2.2.The local structure of the moduli spaces
2.2.3.Generic smoothness
2.2.4.Orientability
2.3.The structure of the Seiberg-Witten invariants
2.3.1.The universal line bundle
2.3.2.The case b+ > 1
2.3.3.The case b+ = 1
2.3.4.Some examples
2.4.Applications
2.4.1.The Seiberg-Witten equations on cylinders
2.4.2.The Thom conjecture
2,4.3.Negative definite smooth 4-manifolds
Chapter 3.Seiberg-Witten Equations on Complex Surfaces
3.1.A short trip in complex geometry
3.1.1.Basic notions
3.1.2.Examples of complex surfaces
3.1.3.Kodaira classification of complex surfaces
3.2.Seiberg-Witten invariants of Khler surfaces
3.2.1.Seiberg-Witten equations on Kahler surfaces
3.2.2.Monopoles, vortices and divisors
3.2.3.Deformation theory
3.3.Applications
3.3.1.A nonvanishing result
3.3.2.Seiberg-Witten invariants of simply connected elliptic surfaces
3.3.3.The failure of the h-cobordism theorem in four dimensions
3.3.4.Seiberg-Witten equations on symplectic 4-manifolds
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