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1、AlanF.BeardonTheGeometryofDiscreteGroupsWith93IllustrationsSpringerAlanF.BeardonUniversityofCambridgeDepartmentofPureMathematicsandMathematicalStatistics16MillLaneCambridgeCB21SBEnglandEditorialBoardS.AxierF.W.GehringP.R.HalmosDepartmentofDepartmentofD
2、epartmentofMathematicsMathematicsMathematicsMichiganStateUniversityUniversityofMichiganSantaClaraUniversityEastLansing,MI48824AnnArbor,MI48109SantaClara,CA95053USAUSAUSAMathematicsSubjectClassifications(1991):30-01,30CXX,20F32,30FXX,51Mb,20HXXLibraryof
3、CongressCataloginginPublicationDataBeardon,AlanF.Thegeometryofdiscretegroups.(Graduatetextsinmathematics;91)Includesbibliographicalreferencesandindex.1.Discretegroups.2.Isometries(Mathematics)3.Möbiustransformations.4.Geometry,Hyperbolic.I.Title.II.Ser
4、ies.QA17I.B3641983512'.282-19268©1983bySpringer-VerlagNewYorkInc.Allrightsreserved.NopartofthisbookmaybetranslatedorreproducedinanyformwithoutwrittenpermissionfromSpringer-Verlag,175FifthAvenue,NewYork,NewYork10010,U.S.A.TypesetbyCompositionHouseLtd.,S
5、alisbury,England.PrintedandboundbyR.R.Donnelley&Sons,Harrisonburg,VA.PrintedintheUnitedStatesofAmerica.98765432(Correctedsecondprinting,1995)ISBN0-387-90788-2Springer-VerlagNewYorkHeidelbergBerlinISBN3-540-90788-2Springer-VerlagBerlinHeidelbergNewYorkT
6、oToniPrefaceThistextisintendedtoserveasanintroductiontothegeometryoftheactionofdiscretegroupsofMöbiustransformations.Thesubjectmatterhasnowbeenstudiedwithchangingpointsofemphasisforoverahundredyears,themostrecentdevelopmentsbeingconnectedwiththetheoryo
7、f3-manifolds:see,forexample,thepapersofPoiricaré[77]andThurston[101].About1940,thenowwell-known(butvirtuallyunobtainable)Fenchel—Nielsenmanuscriptappeared.Sadly,themanuscriptneverappearedinprint,andthismoremodesttextattemptstodisplayatleastsomeofthebea
8、utifulgeo-metricalideastobefoundinthatmanuscript,aswellassomemorerecentmaterial.Thetexthasbeenwrittenwiththeconvictionthatgeometricalexplana-tionsareessentialforafullunderstandingofthematerialandthathoweversimpleamatrixproofmightseem,ag
