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1、TopologicalEmbeddingsThisisVolume52inPUREANDAPPLIEDMATHEMATICSAseriesofMonographsandTextbooksEditors:PAULA.SMITHANDSAMUELEILENBERGAcompletelistoftitlesinthisseriesappearsattheendofthisvolumeTopologiculEmbeddingsT.BENNYRUSHINGDepartmentofMathematicsUniversityofUtahSultLakeCity@ACADEMICPRE
2、SS1973NewYorkandLondonCOPYRIGHT01973,BYACADEMICPRESS,INC.ALLRIGHTSRESERVED.NOPARTOFTHISPUBLICATIONMAYBEREPRODUCEDORTRANSMITTEDINANYFORMORBYANYMEANS,ELECTRONICORMECHANICAL,INCLUDINGPHOTOCOPY,RECORDING,ORANYINFORMATIONSTORAGEANDRETRIEVALSYSTEM,WITHOUTPERMISSIONINWRITINGFROMTHEPUBLISHER.ACA
3、DEMICPRESS,INC.111FifthAvenue,NewYork,NewYork10003UniiedKingdomEdiiionpublishedbyACADEMICPRESS,INC.(LONDON)LTD.24/28OvalRoad,LondonNWlLIBRARYOFCONGRESSCATALOGCARDNUMBER:72-71344AMS(MOS)1970SubjectClassifications:57A.57CPRINTEDINTHEUNITEDSTATESOFAMERICATotheMemoryofmyMotherCHRISTINEWALTER
4、SRUSH1NG(1913-1970)ThisPageIntentionallyLeftBlankContentsPrefacexi...Acknowledgmentsx111Chapter1.lainProblemandPreiminaryNotions1.1Introduction11.2MainProblem11.3TopologicalManifolds21.4TheCategoryofPolyhedraandPiecewiseLinearMaps41.5MethodofAttackingtheMainProblem81.6PiecewiseLinearMani
5、foldsandPiecewiseLinearTools91.7LocalFlatness,(Pinched)Collars,and(Pinched)Bicollars33I.8CellularSetsandApplications44Chapter2WildEmbeddings,KnottedEmbeddings,andRelatedTopics2.1IntroductoryDefinitions512.2TheGroupofaKnotandKnottedCodimensionTwoSpheres512.3LocalHomotopyGroups,WildCodimen
6、sionTwoCellsandSpheres,andTameNonlocallyFlatCodimensionTwoCellsandSpheres562.4Wild1-Cells,1-Spheres,2-Cells,and2-SpheresinS3602.5EnModuloanArcCrossedwithElIsEn”742.6EverywhereWildCellsandSpheresinEn93ofAllCodimensions842.7SomeWildPolyhedrainLowCodimensions91vii...VlllContentsChapter3Flat
7、tening,Unknotting,andTamingSpecialEmbeddings3.1Introduction983.2AlmostPolyhedralArcsAreFlat993.3An(n-1)-SphereinSn>4whichIsLocallyFlatModuloaPointIsFlat1003.4FlatteningCells,Half-Strings,andStrings1053.5PLUnknottingInfinitePolyhedraintheTrivialRange1103.6E(x)-TamingLocall
