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1、AlgorithmsandComputationinMathematics•Volume9EditorsArjehM.CohenHenriCohenDavidEisenbudMichaelF.SingerBerndSturmfelsSergeiMatveevAlgorithmicTopologyandClassificationof3-ManifoldsSecondEditionWith264Figuresand36TablesABCAuthorSergeiMatveevChelyabinskStateUniversityKashirinBrothersStreet,
2、129Chelyabinsk454021RussiaE-mail:matveev@csu.ruLibraryofCongressControlNumber:2007927936MathematicsSubjectClassification(2000):57MISSN1431-1550ISBN978-3-540-45898-2SpringerBerlinHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcern
3、ed,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversio
4、n,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediaspringer.comcSpringer-VerlagBerlinHeidelberg2007Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicati
5、ondoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.TypesettingbytheauthorandSPiusingaSpringerLATEXmacropackageCoverdesign:design&productionGmbH,HeidelbergPrintedonacid-freepaperSPIN:1187981746
6、/SPi543210PrefacetotheFirstEditionThebookisdevotedtoalgorithmiclow-dimensionaltopology.Thisbranchofmathematicshasrecentlybeenundergoinganintensedevelopment.Ontheonehand,theexponentialadvancementofcomputertechnologieshasmadeitpossibletoconductsophisticatedcomputerexperimentsandtoimplemen
7、talgorithmicsolutions,whichhaveinturnprovidedamotivationtosearchfornewandbetteralgorithms.Ontheotherhand,low-dimensionaltopologyhasreceivedanadditionalboostbecauseofthediscoveryofnumerousconnectionswiththeoreticalphysics.Thereisalsoanotherdeepreasonwhyalgorithmictopologyhasrece
