Kirk P. Davis J.F Lecture notes in algebraic topology

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1、LectureNotesinAlgebraicTopologyJamesF.DavisPaulKirkAuthoraddress:DepartmentofMathematics,IndianaUniversity,Blooming-ton,IN47405E-mailaddress:jfdavis@indiana.edu,pkirk@indiana.edu1991MathematicsSubjectClassification.55-XX.ContentsPrefaceixProjectsxiiiChapter1.ChainComplexes,Homology

2、,andCohomology1§1.1.Chaincomplexesassociatedtoaspace1§1.2.Tensorproducts,adjointfunctors,andHom7§1.3.TensorandHomfunctorsonchaincomplexes12§1.4.Singularcohomology14§1.5.TheEilenberg-Steenrodaxioms19§1.6.ProjectsforChapter121Chapter2.HomologicalAlgebra23§2.1.AxiomsforTorandExt;proj

3、ectiveresolutions23§2.2.Projectiveandinjectivemodules29§2.3.Resolutions32§2.4.DefinitionofTorandExt-existence35§2.5.Thefundamentallemmaofhomologicalalgebra36§2.6.Universalcoefficienttheorems43§2.7.ProjectsforChapter249Chapter3.Products51iiiivContents§3.1.Tensorproductsofchaincomplexe

4、sandthealgebraicK¨unneththeorem51§3.2.TheEilenberg-Zilbermaps54§3.3.Crossandcupproducts56§3.4.TheAlexander-Whitneydiagonalapproximation64§3.5.Relativecupandcapproducts67§3.6.ProjectsforChapter370Chapter4.FiberBundles77§4.1.Groupactions77§4.2.Fiberbundles78§4.3.Examplesoffiberbundle

5、s81§4.4.Principalbundlesandassociatedbundles84§4.5.Reducingthestructuregroup89§4.6.Mapsofbundlesandpullbacks90§4.7.ProjectsforChapter492Chapter5.HomologywithLocalCoefficients95§5.1.Definitionofhomologywithtwistedcoefficients96§5.2.Examplesandbasicproperties98§5.3.Definitionofhomologywit

6、halocalcoefficientsystem103§5.4.Functoriality105§5.5.ProjectsforChapter5108Chapter6.Fibrations,CofibrationsandHomotopyGroups111§6.1.Compactlygeneratedspaces111§6.2.Fibrations114§6.3.Thefiberofafibration116§6.4.Pathspacefibrations120§6.5.Fiberhomotopy123§6.6.Replacingamapbyafibration123§6

7、.7.Cofibrations127Contentsv§6.8.Replacingamapbyacofibration131§6.9.Setsofhomotopyclassesofmaps134§6.10.Adjointofloopsandsuspension;smashproducts136§6.11.Fibrationandcofibrationsequences139§6.12.Puppesequences142§6.13.Homotopygroups144§6.14.Examplesoffibrations146§6.15.Relativehomotopy

8、groups153§6.16.Theactionofthefund