algebraic l theory and topological manifold

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1、ALGEBRAICL-THEORYANDTOPOLOGICALMANIFOLDSA.A.RanickiUniversityofEdinburghThisisthefulltextofthebookpublishedin1992asVolume102oftheCambridgeTractsinMathematicsbytheCambridgeUniversityPress,withsomecorrectionsandadditionalmaterial.ThelistofchangesismaintainedonmyWWWHomePage:http://www.maths.ed.ac.

2、uk/~aarPleasesendanyfurthersuggestionsforimprovements,preferablybye-mailto:aar@maths.ed.ac.ukMarch,2001ContentsIntroduction1Summary21PartI.Algebrax1.AlgebraicPoincarecomplexes25x2.Algebraicnormalcomplexes38x3.Algebraicbordismcategories51x4.Categoriesovercomplexes63x5.Duality74x6.Simplyconnecte

3、dassembly80x7.DerivedproductandHom85x8.LocalPoincareduality89x9.Universalassembly94x10.Thealgebraic-theorem109x11.
-sets117x12.Generalizedhomologytheory122x13.AlgebraicL-spectra134x14.Thealgebraicsurgeryexactsequence144x15.ConnectiveL-theory151PartII.Topologyx16.TheL-theoryorientationoftopol

4、ogy173x17.Thetotalsurgeryobstruction189x18.Thestructureset195x19.GeometricPoincarecomplexes202x20.Thesimplyconnectedcase209x21.Transfer214x22.Finitefundamentalgroup221x23.Splitting257x24.Highersignatures269x25.The4-periodictheory284x26.Surgerywithcoecients302AppendixA.Thenonorientablecase307A

5、ppendixB.Assemblyviaproducts317AppendixC.Assemblyviaboundedtopology323Bibliography343Index354PrefaceThealgebraicL-theoryofquadraticformsrelatesthetopologyofmanifoldstotheirhomotopytypes.Thistractprovidesareasonablyself-containedac-countofthisrelationshipindimensions5,whichwasestablishedover20y

6、earsagobytheBrowder{Novikov{Sullivan{Wallsurgerytheoryforcom-pactdierentiableandPLmanifolds,andextendedtotopologicalmanifoldsbyKirbyandSiebenmann.Theterm`algebraicL-theory'wascoinedbyWall,tomeanthealgebraicK-theoryofquadraticforms,aliashermitianK-theory.Intheclassicaltheoryofquadraticformstheg

7、roundringisaeld,oraringofintegersinanalgebraicnumbereld,andquadraticformsareclassieduptoisomorphism.InalgebraicL-theoryitisnecessarytoconsiderquadraticformsovermoregeneralrings,butonlyuptostableisomorphism.Intheapplicationstoto