资源描述:
《gtm091.the.geometry.of.discrete.groups,.beardon.a.f..(springer.1995)(isbn.3540907882)(t)(347s)》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、AlanF.BeardonTheGeometryofDiscreteGroupsWith93IllustrationsSpringerAlanF.BeardonUniversityofCambridgeDepartmentofPureMathematicsandMathematicalStatistics16MillLaneCambridgeCB21SBEnglandEditorialBoardS.AxierF.W.GehringP.R.HalmosDepartmentofDepartmentofDepa
2、rtmentofMathematicsMathematicsMathematicsMichiganStateUniversityUniversityofMichiganSantaClaraUniversityEastLansing,MI48824AnnArbor,MI48109SantaClara,CA95053USAUSAUSAMathematicsSubjectClassifications(1991):30-01,30CXX,20F32,30FXX,51Mb,20HXXLibraryofCongre
3、ssCataloginginPublicationDataBeardon,AlanF.Thegeometryofdiscretegroups.(Graduatetextsinmathematics;91)Includesbibliographicalreferencesandindex.1.Discretegroups.2.Isometries(Mathematics)3.Möbiustransformations.4.Geometry,Hyperbolic.I.Title.II.Series.QA17I
4、.B3641983512'.282-19268©1983bySpringer-VerlagNewYorkInc.Allrightsreserved.NopartofthisbookmaybetranslatedorreproducedinanyformwithoutwrittenpermissionfromSpringer-Verlag,175FifthAvenue,NewYork,NewYork10010,U.S.A.TypesetbyCompositionHouseLtd.,Salisbury,Eng
5、land.PrintedandboundbyR.R.Donnelley&Sons,Harrisonburg,VA.PrintedintheUnitedStatesofAmerica.98765432(Correctedsecondprinting,1995)ISBN0-387-90788-2Springer-VerlagNewYorkHeidelbergBerlinISBN3-540-90788-2Springer-VerlagBerlinHeidelbergNewYorkToToniPrefaceThi
6、stextisintendedtoserveasanintroductiontothegeometryoftheactionofdiscretegroupsofMöbiustransformations.Thesubjectmatterhasnowbeenstudiedwithchangingpointsofemphasisforoverahundredyears,themostrecentdevelopmentsbeingconnectedwiththetheoryof3-manifolds:see,f
7、orexample,thepapersofPoiricaré[77]andThurston[101].About1940,thenowwell-known(butvirtuallyunobtainable)Fenchel—Nielsenmanuscriptappeared.Sadly,themanuscriptneverappearedinprint,andthismoremodesttextattemptstodisplayatleastsomeofthebeautifulgeo-metricalide
8、astobefoundinthatmanuscript,aswellassomemorerecentmaterial.Thetexthasbeenwrittenwiththeconvictionthatgeometricalexplana-tionsareessentialforafullunderstandingofthematerialandthathoweversimpleamatrixproofmightseem,ag