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1、AlgorithmsandComputationinMathematics•Volume21EditorsArjehM.CohenHenriCohenDavidEisenbudMichaelF.SingerBerndSturmfelsDmitryKozlovCombinatorialAlgebraicTopologyWith115Figuresand1TableABCAuthorDmitryKozlovFachbereich3-MathematikUniversityofBremen28334BremenGermany
2、E-mail:dfk@math.uni-bremen.deLibraryofCongressControlNumber:2007933072MathematicsSubjectClassification(2000):55U10,06A07,05C15.ISSN1431-1550ISBN978-3-540-71961-8SpringerBerlinHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpart
3、ofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanC
4、opyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediaspringer.comcSpringer-VerlagBerlinHeidelberg2008Theuse
5、ofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.TypesettingbytheauthorandSPiusingaSpringerLA
6、TEXmacropackageCoverdesign:WMXDesign,HeidelbergPrintedonacid-freepaperSPIN:1193675646/SPi543210DedicatedtomyfamilyPrefaceTheintentofthisbookistointroducethereadertothebeautifulworldofCombinatorialAlgebraicTopology.Whilethemainpurposeistodescribethemodernresearch
7、toolsandlatestapplicationsofthisfield,anattempthasbeenmadetokeepthepresentationasself-containedaspossible.AbooktoteachfromThetextisdividedintothreemajorparts,whichprovideseveraloptionsforadoptionforcoursepurposes,dependingonthetimeavailabletotheinstruc-tor.Thefirs
8、tpartfurnishesabriskwalkthroughsomeofthebasicconceptsofalgebraictopology.Whileitisinnowaymeanttoreplaceastandardcourseinthatfield,itcouldprovehelpfulatthebeginningofth
