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1、LectureNotesinAlgebraicTopologyJamesF.DavisPaulKirkAuthoraddress:DepartmentofMathematics,IndianaUniversity,Blooming-ton,IN47405E-mailaddress:jfdavis@indiana.edu,pkirk@indiana.edu1991MathematicsSubjectClassi?cation.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.De?nitionofTorandExt-existence35§2.5.Thefundamentallemmaofhomologicalalgebra36§2.6.Universalcoe?cienttheorems43§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.Examplesof?berbundle
5、s81§4.4.Principalbundlesandassociatedbundles84§4.5.Reducingthestructuregroup89§4.6.Mapsofbundlesandpullbacks90§4.7.ProjectsforChapter492Chapter5.HomologywithLocalCoe?cients95§5.1.De?nitionofhomologywithtwistedcoe?cients96§5.2.Examplesandbasicproperties98§5.3.De?nitionofhomologywit
6、halocalcoe?cientsystem103§5.4.Functoriality105§5.5.ProjectsforChapter5108Chapter6.Fibrations,Co?brationsandHomotopyGroups111§6.1.Compactlygeneratedspaces111§6.2.Fibrations114§6.3.The?berofa?bration116§6.4.Pathspace?brations120§6.5.Fiberhomotopy123§6.6.Replacingamapbya?bration123§6
7、.7.Co?brations127Contentsv§6.8.Replacingamapbyaco?bration131§6.9.Setsofhomotopyclassesofmaps134§6.10.Adjointofloopsandsuspension;smashproducts136§6.11.Fibrationandco?brationsequences139§6.12.Puppesequences142§6.13.Homotopygroups144§6.14.Examplesof?brations146§6.15.Relativehomotopy
8、groups153§6.16.Theactionofthefund
