书目

AlgebraicL-theoryandTopologicalManifolds(CambridgeTractsinMathematics)

内容简介

ThisbookpresentsadefinitiveaccountoftheapplicationsofthealgebraicL-theorytothesurgeryclassificationoftopologicalmanifolds.ThecentralresultistheidentificationofamanifoldstructureinthehomotopytypeofaPoincarédualityspacewithalocalquadraticstructureinthechainhomotopytypeoftheuniversalcover.ThedifferencebetweenthehomotopytypesofmanifoldsandPoincarédualityspacesisidentifiedwiththefibreofthealgebraicL-theoryassemblymap,whichpassesfromlocaltoglobalquadraticdualitystructuresonchaincomplexes.ThealgebraicL-theoryassemblymapisusedtogiveapurelyalgebraicformulationoftheNovikovconjecturesonthehomotopyinvarianceofthehighersignatures;anyotherformulationnecessarilyfactorsthroughthisone.Thebookisdesignedasanintroductiontothesubject,accessibletograduatestudentsintopology;nopreviousacquaintancewithsurgerytheoryisassumed,andeveryalgebraicconceptisjustifiedbyitsoccurrenceintopology.

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