层论

图书标准信息

• 作者 [美]布里登 著
• 出版社 世界图书出版公司
• 出版时间 2010-01
• 版次 1
• ISBN 9787510004698
• 定价 60.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 502页
• 正文语种 英语

【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。

【目录】

Preface
ISheavesandPresheaves
1Definitions
2Homomorphisms，subsheaves，andquotientsheaves
3Directandinverseimages
4Cohomomorphisms
5Algebraicconstructions
6Supports
7Classicalcohomologytheories
Exercises

IISheafCohomology
IDifferentialsheavesandresolutions
2Thecanonicalresolutionandsheafcohomology
3Injectivesheaves
4Acyclicsheaves
5Flabbysheaves
6Connectedsequencesoffunctors
7Axiomsforcohomologyandthecupproduct
8Mapsofspaces
9φ-softandφ-finesheaves
10Subspaces
11TheVietorismappingtheoremandhomotopyinvariance
12Relativecohomology
13Mayer-Vietoristheorems
14Continuity
15TheKiinnethanduniversalcoefficienttheorems
16Dimension
17Localconnectivity
18Changeofsupports;localcohomologygroups
19ThetransferhomomorphismandtheSmithsequences
20Steenrodscyclicreducedpowers
21TheSteenrodoperations
Exercises

IIIComparisonwithOtherCohomologyTheories
1Singularcohomology
2Alexander-Spaniercohomology
3deRhamcohomology
4Cechcohomology
Exercises

IVApplicationsofSpectralSequerices
IThespectralsequenceofadifferentialsheaf
2Thefundamentaltheoremsofsheaves
3Directimagerelativetoasupportfamily
4TheLeraysheaf
5Extensionofasupportfamilybyafamilyonthebasespace
6TheLerayspectralsequenceofamap
7Fiberbundles
8Dimension
9ThespectralsequencesofBorelandCaftan
10Characteristicclasses
11Thespectralsequenceofafiltereddifferentialsheaf
12TheFaryspectralsequence
13Spherebundleswithsingularities
14TheOlivertransferandtheConnerconjecture
Exercises

VBorel-UooreHomology
ICosheaves
2Thedualofadifferentialcosheaf
3Homologytheory
4Mapsofspaces
5Subspacesandrelativehomology
6TheVietoristheorem，homotopy，andcoveringspaces
7Thehomologysheafofamap
8Thebasicspectralsequences
9Poincareduality
10Thecapproduct
11Intersectiontheory
12Uniquenesstheorems
13Uniquenesstheoremsformapsandrelativehomology
14TheKuinnethformula
15Changeofrings
16Generalizedmanifolds
17Locallyhomogeneousspaces
18Homologicalfibrationsandp-adictransformationgroups
19Thetransferhomomorphisminhomology
20Smiththeoryinhomology
Exercises

VICosheavesandCechHomology
ITheoryofcosheaves
2Localtriviality
3Localisomorphisms
4Cechhomology
5Thereflector
6Spectralsequences
7Coresolutions
8RelativeCechhomology
9Locallyparacompactspaces
10Borel-Moorehomology
11ModifiedBorel-Moorehomology
12Singularhomology
13Acycliccoverings
14Applicationstomaps
Exercises

ASpectralSequences
1Thespectralsequenceofafilteredcomplex
2Doublecomplexes
3Products
4Homomorphisms

BSolutionstoSelectedExercises
SolutionsforChapterI
SolutionsforChapterII
SolutionsforChapterIII
SolutionsforChapterIV
SolutionsforChapterV
SolutionsforChapterVI
Bibliography
ListofSymbols
ListofSelectedFacts
Index