层论与紧黎曼曲面(Sheaf Theory)扫描版[DJVU]

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资源信息： 中文名: 层论与紧黎曼曲面 原名: Sheaf Theory 作者: Bredon 图书分类: 科技 资源格式: DJVU 版本: 扫描版 出版社: Springer 书号: 0387949054 发行时间: 1997年 地区: 美国 语言: 英文 概述:

djvu 阅读器： 　http://windjview.sourceforge.net/ 内容简介: 本书主要讲述具有一般系数体系拓扑空间的上同调理论。层论包括对代数拓扑很重要的领域。书中有好多创新点，引进不少新概念，全书内容贯穿一致。证实了广义同调空间中层理论上同调满足同调基本特性的事实。将相对上同调引入层理论中。 　　读者有一定的基本同调代数和代数拓扑知识就可以理解本书。每章末都附有练习，这些可以帮助学生更好的理解书中的知识体系。附录给出了部分习题的解答。第二版中在内容上做了较大的改动，增加了80多例子和大量更深层次的内容，如，Cech上同调、Oliver变换、插值理论、广义流形、局部齐性空间、同调纤维和p进变换群。目次：层和准层；层上同调；与其他上同调定理的比较；谱序列的应用；Borel- Moore同调；上层和ech同调。 　　读者对象：数学专业的高年级本科生、研究生和相关专业的学者。 内容截图:

目录: Preface I Sheaves and Presheaves 1 Definitions 2 Homomorphisms, subsheaves, and quotient sheaves 3 Direct and inverse images 4 Cohomomorphisms 5 Algebraic constructions 6 Supports 7 Classical cohomology theories Exercises II Sheaf Cohomology I Differential sheaves and resolutions 2 The canonical resolution and sheaf cohomology 3 Injective sheaves 4 Acyclic sheaves 5 Flabby sheaves 6 Connected sequences of functors 7 Axioms for cohomology and the cup product 8 Maps of spaces 9 φ-soft and φ-fine sheaves 10 Subspaces 11 The Vietoris mapping theorem and homotopy invariance 12 Relative cohomology 13 Mayer-Vietoris theorems 14 Continuity 15 The Kiinneth and universal coefficient theorems 16 Dimension 17 Local connectivity 18 Change of supports; local cohomology groups 19 The transfer homomorphism and the Smith sequences 20 Steenrod's cyclic reduced powers 21 The Steenrod operations Exercises III Comparison with Other Cohomology Theories 1 Singular cohomology 2 Alexander-Spanier cohomology 3 de Rham cohomology 4 Cech cohomology Exercises IV Applications of Spectral Sequerices I The spectral sequence of a differential sheaf 2 The fundamental theorems of sheaves 3 Direct image relative to a support family 4 The Leray sheaf 5 Extension of a support family by a family on the base space 6 The Leray spectral sequence of a map 7 Fiber bundles 8 Dimension 9 The spectral sequences of Borel and Caftan 10 Characteristic classes 11 The spectral sequence of a filtered differential sheaf 12 The Fary spectral sequence 13 Sphere bundles with singularities 14 The Oliver transfer and the Conner conjecture Exercises V Borel-Uoore Homology I Cosheaves 2 The dual of a differential cosheaf 3 Homology theory 4 Maps of spaces 5 Subspaces and relative homology 6 The Vietoris theorem, homotopy, and covering spaces 7 The homology sheaf of a map 8 The basic spectral sequences 9 Poincare duality 10 The cap product 11 Intersection theory 12 Uniqueness theorems 13 Uniqueness theorems for maps and relative homology 14 The Kuinneth formula 15 Change of rings 16 Generalized manifolds 17 Locally homogeneous spaces 18 Homological fibrations and p-adic transformation groups 19 The transfer homomorphism in homology 20 Smith theory in homology Exercises VI Cosheaves and Cech Homology I Theory of cosheaves 2 Local triviality 3 Local isomorphisms 4 Cech homology 5 The reflector 6 Spectral sequences 7 Coresolutions 8 Relative Cech homology 9 Locally paracompact spaces 10 Borel-Moore homology 11 Modified Borel-Moore homology 12 Singular homology 13 Acyclic coverings 14 Applications to maps Exercises A Spectral Sequences 1 The spectral sequence of a filtered complex 2 Double complexes 3 Products 4 Homomorphisms B Solutions to Selected Exercises Solutions for Chapter I Solutions for Chapter II Solutions for Chapter III Solutions for Chapter IV Solutions for Chapter V Solutions for Chapter VI Bibliography List of Symbols List of Selected Facts Index