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1、SpringerMonographsinMathematicsM.BanaglTopologicalInvariantsofStratifiedSpacesM.BanaglMathematischesInstitutUniversitätHeidelbergImNeuenheimerFeld28869120Heidelberg,Germanye-mail:banagl@mathi.uni-heidelberg.deLibraryofCongressControlNumber:2006693517MathematicsSubject
2、Classification(2000):55N33ISSN1439-7382ISBN-103-540-38585-1SpringerBerlinHeidelbergNewYorkISBN-13978-3-540-38585-1SpringerBerlinHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftrans
3、lation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermi
4、ssionforusemustalwaysbeobtainedfromSpringer.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediaspringer.comcSpringer-VerlagBerlinHeidelberg2007Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthi
5、spublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.TypesettingbytheauthorandVTEXusingaSpringerLATEXmacropackageCoverdesign:ErichKirchner,Heidelberg,GermanyPrinted
6、onacid-freepaperSPIN:11839545VA44/3100/VTEX-543210PrefaceThehomologyofmanifoldsenjoysaremarkablesymmetry:Poincaréduality.Ifthemanifoldistriangulated,thenthisdualitycanbeestablishedbyassociatingtoasim-plexitsdualblockinthebarycentricsubdivision.Inamanifold,thedualbloc
7、kisacell,sothechaincomplexbasedonthedualblockscomputesthehomologyofthemanifold.Poincarédualitythenservesasacornerstoneofmanifoldclassificationtheory.Onereasonisthatitenablesthedefinitionofafundamentalbordisminvari-ant,thesignature.Classifyingmanifoldsviathesurgeryprogr
8、amreliesonmodifyingamanifoldbyexecutinggeometricsurgeries.Thetraceofthesurgeryisabordismbetweentheoriginalmanifoldandtheresultofsur
