Kleinian groups and hyperbolic 3-manifolds PDF
Preview Kleinian groups and hyperbolic 3-manifolds
This page intentionally left blank LONDONMATHEMATICALSOCIETYLECTURENOTESERIES ManagingEditor:ProfessorN.J.Hitchin,MathematicalInstitute, UniversityofOxford,24–29StGiles,OxfordOX13LB,UnitedKingdom Thetitlesbelowareavailablefrombooksellers,or,incaseofdifficulty,fromCambridgeUniversityPress atwww.cambridge.org. 121 ProceedingsofGroups–StAndrews1985, E.ROBERTSON&C.CAMPBELL(eds) 128 Descriptivesettheoryandthestructureofsetsofuniqueness, A.S.KECHRIS&A.LOUVEAU 130 Modeltheoryandmodules, M.PREST 131 Algebraic,extremal&metriccombinatorics, M.-M.DEZA,P.FRANKL&I.G.ROSENBERG(eds) 138 AnalysisatUrbana,II, E.BERKSON,T.PECK,&J.UHL(eds) 139 Advancesinhomotopytheory, S.SALAMON,B.STEER&W.SUTHERLAND(eds) 140 GeometricaspectsofBanachspaces, E.M.PEINADOR&A.RODES(eds) 141 Surveysincombinatorics1989, J.SIEMONS(ed) 144 Introductiontouniformspaces, I.M.JAMES 146 Cohen-MacaulaymodulesoverCohen-Macaulayrings, Y.YOSHINO 148 Helicesandvectorbundles, A.N.RUDAKOVetal 149 Solitons,nonlinearevolutionequationsandinversescattering, M.ABLOWITZ&P.CLARKSON 150 Geometryoflow-dimensionalmanifolds1, S.DONALDSON&C.B.THOMAS(eds) 151 Geometryoflow-dimensionalmanifolds2, S.DONALDSON&C.B.THOMAS(eds) 152 Oligomorphicpermutationgroups, P.CAMERON 153 L-functionsandarithmetic, J.COATES&M.J.TAYLOR(eds) 155 Classificationtheoriesofpolarizedvarieties, TAKAOFUJITA 158 GeometryofBanachspaces, P.F.X.MU¨LLER&W.SCHACHERMAYER(eds) 159 GroupsStAndrews1989volume1, C.M.CAMPBELL&E.F.ROBERTSON(eds) 160 GroupsStAndrews1989volume2, C.M.CAMPBELL&E.F.ROBERTSON(eds) 161 Lecturesonblocktheory, BURKHARDKU¨LSHAMMER 163 Topicsinvarietiesofgrouprepresentations, S.M.VOVSI 164 Quasi-symmetricdesigns, M.S.SHRIKANDE&S.S.SANE 166 Surveysincombinatorics,1991, A.D.KEEDWELL(ed) 168 Representationsofalgebras, H.TACHIKAWA&S.BRENNER(eds) 169 Booleanfunctioncomplexity, M.S.PATERSON(ed) 170 ManifoldswithsingularitiesandtheAdams-Novikovspectralsequence, B.BOTVINNIK 171 Squares, A.R.RAJWADE 172 Algebraicvarieties, GEORGER.KEMPF 173 Discretegroupsandgeometry, W.J.HARVEY&C.MACLACHLAN(eds) 174 Lecturesonmechanics, J.E.MARSDEN 175 Adamsmemorialsymposiumonalgebraictopology1, N.RAY&G.WALKER(eds) 176 Adamsmemorialsymposiumonalgebraictopology2, N.RAY&G.WALKER(eds) 177 Applicationsofcategoriesincomputerscience, M.FOURMAN,P.JOHNSTONE&A.PITTS(eds) 178 LowerK-andL-theory, A.RANICKI 179 Complexprojectivegeometry, G.ELLINGSRUDetal 180 LecturesonergodictheoryandPesintheoryoncompactmanifolds, M.POLLICOTT 181 GeometricgrouptheoryI, G.A.NIBLO&M.A.ROLLER(eds) 182 GeometricgrouptheoryII, G.A.NIBLO&M.A.ROLLER(eds) 183 Shintanizetafunctions, A.YUKIE 184 Arithmeticalfunctions, W.SCHWARZ&J.SPILKER 185 Representationsofsolvablegroups, O.MANZ&T.R.WOLF 186 Complexity:knots,colouringsandcounting, D.J.A.WELSH 187 Surveysincombinatorics,1993, K.WALKER(ed) 188 Localanalysisfortheoddordertheorem, H.BENDER&G.GLAUBERMAN 189 Locallypresentableandaccessiblecategories, J.ADAMEK&J.ROSICKY 190 Polynomialinvariantsoffinitegroups, D.J.BENSON 191 Finitegeometryandcombinatorics, F.DECLERCKetal 192 Symplecticgeometry, D.SALAMON(ed) 194 Independentrandomvariablesandrearrangementinvariantspaces, M.BRAVERMAN 195 Arithmeticofblowupalgebras, WOLMERVASCONCELOS 196 Microlocalanalysisfordifferentialoperators, A.GRIGIS&J.SJO¨STRAND 197 Two-dimensionalhomotopyandcombinatorialgrouptheory, C.HOG-ANGELONIetal 198 Thealgebraiccharacterizationofgeometric4-manifolds, J.A.HILLMAN 199 InvariantpotentialtheoryintheunitballofCn, MANFREDSTOLL 200 TheGrothendiecktheoryofdessinsd’enfant, L.SCHNEPS(ed) 201 Singularities, JEAN-PAULBRASSELET(ed) 202 Thetechniqueofpseudodifferentialoperators, H.O.CORDES 203 HochschildcohomologyofvonNeumannalgebras, A.SINCLAIR&R.SMITH 204 Combinatorialandgeometricgrouptheory, A.J.DUNCAN,N.D.GILBERT&J.HOWIE(eds) 205 Ergodictheoryanditsconnectionswithharmonicanalysis, K.PETERSEN&I.SALAMA(eds) 207 GroupsofLietypeandtheirgeometries, W.M.KANTOR&L.DIMARTINO(eds) 208 Vectorbundlesinalgebraicgeometry, N.J.HITCHIN,P.NEWSTEAD&W.M.OXBURY(eds) 209 Arithmeticofdiagonalhypersurfacesoverfinitefields, F.Q.GOUVEA&N.YUI 210 HilbertC∗-modules, E.C.LANCE 211 Groups93Galway/StAndrewsI, C.M.CAMPBELLetal(eds) 212 Groups93Galway/StAndrewsII, C.M.CAMPBELLetal(eds) 214 GeneralisedEuler-Jacobiinversionformulaandasymptoticsbeyondallorders, V.KOWALENKOetal 215 Numbertheory1992–93, S.DAVID(ed) 216 Stochasticpartialdifferentialequations, A.ETHERIDGE(ed) 217 Quadraticformswithapplicationstoalgebraicgeometryandtopology, A.PFISTER 218 Surveysincombinatorics,1995, PETERROWLINSON(ed) 220 Algebraicsettheory, A.JOYAL&I.MOERDIJK 221 Harmonicapproximation, S.J.GARDINER 222 Advancesinlinearlogic, J.-Y.GIRARD,Y.LAFONT&L.REGNIER(eds) 223 Analyticsemigroupsandsemilinearinitialboundaryvalueproblems, KAZUAKITAIRA 224 Computability,enumerability,unsolvability, S.B.COOPER,T.A.SLAMAN&S.S.WAINER(eds) 225 Amathematicalintroductiontostringtheory, S.ALBEVERIO,J.JOST,S.PAYCHA,S.SCARLATTI 226 Novikovconjectures,indextheoremsandrigidityI, S.FERRY,A.RANICKI&J.ROSENBERG(eds) 227 Novikovconjectures,indextheoremsandrigidityII, S.FERRY,A.RANICKI&J.ROSENBERG(eds) 228 ErgodictheoryofZdactions, M.POLLICOTT&K.SCHMIDT(eds) 229 Ergodicityforinfinitedimensionalsystems, G.DAPRATO&J.ZABCZYK 230 Prolegomenatoamiddlebrowarithmeticofcurvesofgenus2, J.W.S.CASSELS&E.V.FLYNN 231 Semigrouptheoryanditsapplications, K.H.HOFMANN&M.W.MISLOVE(eds) 232 ThedescriptivesettheoryofPolishgroupactions, H.BECKER&A.S.KECHRIS 233 Finitefieldsandapplications, S.COHEN&H.NIEDERREITER(eds) 234 Introductiontosubfactors, V.JONES&V.S.SUNDER 235 Numbertheory1993–94, S.DAVID(ed) 236 TheJamesforest, H.FETTER&B.GAMBOADEBUEN 237 Sievemethods,exponentialsums,andtheirapplicationsinnumbertheory, G.R.H.GREAVESetal 238 Representationtheoryandalgebraicgeometry, A.MARTSINKOVSKY&G.TODOROV(eds) 239 Cliffordalgebrasandspinors, P.LOUNESTO 240 Stablegroups, FRANK.O.WAGNER 241 Surveysincombinatorics,1997, R.A.BAILEY(ed) 242 GeometricGaloisactionsI, L.SCHNEPS&P.LOCHAK(eds) 243 GeometricGaloisactionsII, L.SCHNEPS&P.LOCHAK(eds) 244 Modeltheoryofgroupsandautomorphismgroups, D.EVANS(ed) 245 Geometry,combinatorialdesignsandrelatedstructures, J.W.P.HIRSCHFELDetal 246 p-Automorphismsoffinitep-groups, E.I.KHUKHRO 247 Analyticnumbertheory, Y.MOTOHASHI(ed) 248 Tametopologyando-minimalstructures, LOUVANDENDRIES 249 Theatlasoffinitegroups:tenyearson, ROBERTCURTIS&ROBERTWILSON(eds) 250 Charactersandblocksoffinitegroups, G.NAVARRO 251 Gro¨bnerbasesandapplications, B.BUCHBERGER&F.WINKLER(eds) 252 Geometryandcohomologyingrouptheory, P.KROPHOLLER,G.NIBLO,R.STO¨HR(eds) 253 Theq-Schuralgebra, S.DONKIN 254 Galoisrepresentationsinarithmeticalgebraicgeometry, A.J.SCHOLL&R.L.TAYLOR(eds) 255 Symmetriesandintegrabilityofdifferenceequations, P.A.CLARKSON&F.W.NIJHOFF(eds) 256 AspectsofGaloistheory, HELMUTVO¨LKLEINetal 257 Anintroductiontononcommutativedifferentialgeometryanditsphysicalapplications2ed, J.MADORE 258 Setsandproofs, S.B.COOPER&J.TRUSS(eds) 259 Modelsandcomputability, S.B.COOPER&J.TRUSS(eds) 260 GroupsStAndrews1997inBath,I, C.M.CAMPBELLetal 261 GroupsStAndrews1997inBath,II, C.M.CAMPBELLetal 263 Singularitytheory, BILLBRUCE&DAVIDMOND(eds) 264 Newtrendsinalgebraicgeometry, K.HULEK,F.CATANESE,C.PETERS&M.REID(eds) 265 Ellipticcurvesincryptography, I.BLAKE,G.SEROUSSI&N.SMART 267 Surveysincombinatorics,1999, J.D.LAMB&D.A.PREECE(eds) 268 Spectralasymptoticsinthesemi-classicallimit, M.DIMASSI&J.SJO¨STRAND 269 Ergodictheoryandtopologicaldynamics, M.B.BEKKA&M.MAYER 270 AnalysisonLieGroups, N.T.VAROPOULOS&S.MUSTAPHA 271 Singularperturbationsofdifferentialoperators, S.ALBEVERIO&P.KURASOV 272 Charactertheoryfortheoddorderfunction, T.PETERFALVI 273 Spectraltheoryandgeometry, E.B,DAVIES&Y.SAFAROV(eds) 274 TheMandelbrotset,themeandvariations, TANLEI(ed) 275 Computationalandgeometricaspectsofmodernalgebra, M.D.ATKINSONetal(eds) 276 Singularitiesofplanecurves, E.CASAS-ALVERO 277 Descriptivesettheoryanddynamicalsystems, M.FOREMANetal(eds) 278 Globalattractorsinabstractparabolicproblems, J.W.CHOLEWA&T.DLOTKO 279 Topicsinsymbolicdynamicsandapplications, F.BLANCHARD,A.MAASS&A.NOGUEIRA(eds) 280 CharactersandAutomorphismGroupsofCompactRiemannSurfaces, T.BREUER 281 Explicitbirationalgeometryof3-folds, ALESSIOCORTI&MILESREID(eds) 282 Auslander-Buchweitzapproximationsofequivariantmodules, M.HASHIMOTO 283 Nonlinearelasticity, R.OGDEN&Y.FU(eds) 284 Foundationsofcomputationalmathematics, R.DEVORE,A.ISERLES&E.SULI(eds) 285 Rationalpointsoncurvesoverfinitefields:TheoryandApplications, H.NIEDERREITER&C.XING 286 Cliffordalgebrasandspinors2ndedn, P.LOUNESTO 287 TopicsonRiemannsurfacesandFuchsiangroups, E.BUJALANCE,A.F.COSTA&E.MARTINEZ(eds) 288 Surveysincombinatorics,2001, J.W.P.HIRSCHFELD(ed) 289 AspectsofSobolev-typeinequalities, L.SALOFF-COSTE 290 QuantumgroupsandLietheory, A.PRESSLEY 291 Titsbuildingsandthemodeltheoryofgroups, K.TENT 292 Aquantumgroupsprimer, S.MAJID 293 SecondorderpartialdifferentialequationsinHilbertspaces,... G.DAPRATO&J.ZABCZYK 294 Introductiontooperatorspacetheory, G.PISIER 296 Lecturesoninvarianttheory, I.DOLGACHEV 297 Thehomotopycategoryofsimplyconnected4-manifolds, H.-J.BAUES LondonMathematicalSocietyLectureNoteSeries.299 Kleinian Groups and Hyperbolic 3-Manifolds Edited by Y. Komori OsakaCityUniversity,Japan V. Markovic UniversityofWarwick C. Series UniversityofWarwick Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge , United Kingdom Published in the United States by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521539319 © T. Brzezinski & R. Wisbauer 2003 This book is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2003 ISBN-13 978-0-511-06562-0 eBook (NetLibrary) ISBN-10 0-511-06562-0 eBook (NetLibrary) ISBN-13 978-0-521-53931-9 paperback ISBN-10 0-521-53931-5 paperback Cambridge University Press has no responsibility for the persistence or accuracy of s for external or third-party internet websites referred to in this book, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Preface pagevii PartI Hyperbolic3-manifolds Combinatorialandgeometricalaspectsofhyperbolic3-manifolds 3 YairN.Minsky Harmonicdeformationsofhyperbolic3-manifolds 41 CraigD.HodgsonandStevenP.Kerckhoff Cone-manifoldsandthedensityconjecture 75 JeffreyF.BrockandKennethW.Bromberg Lesge´ode´siquesferme´esd’unevarie´te´ hyperboliqueentantquenœuds 95 Jean-PierreOtal EndinglaminationsintheMasurdomain 105 GeroKleineidamandJuanSouto Quasi-arcsinthelimitsetofasinglydegenerategroupwithboundedgeometry 131 HidekiMiyachi Onhyperbolicandsphericalvolumesforknotandlinkcone-manifolds 145 AlexanderD.Mednykh Remarksonthecurvecomplex:classificationofsurfacehomeomorphisms 165 W.J.Harvey PartII Once-puncturedtori Onpairsofonce-puncturedtori 183 TroelsJørgensen Comparingtwoconvexhullconstructionsforcuspedhyperbolicmanifolds 209 HirotakaAkiyoshiandMakotoSakuma Jørgensen’spictureofpuncturedtorusgroupsanditsrefinement 247 HirotakaAkiyoshi,MakotoSakuma,MasaakiWadaandYasushiYamashita Tetrahedraldecompositionofpuncturedtorusbundles 275 J.R.Parker OntheboundaryoftheEarlesliceforpuncturedtorusgroups 293 YoheiKomori v vi Contents PartIII Relatedtopics VariationsonathemeofHorowitz 307 JamesW.Anderson Complexanglescaling 343 D.B.A.Epstein,A.MardenandV.Markovic Schwarz’slemmaandtheKobayashiandCarathe´odorypseudometrics oncomplexBanachmanifolds 363 CliffordJ.Earle,LawrenceA.Harris,JohnH.HubbardandSudebMitra Preface ThisvolumeformstheproceedingsoftheworkshopKleinianGroupsandHyperbolic 3- ManifoldswhichwasheldattheMathematicsInstitute,UniversityofWarwick,11–15Septem- ber2001.Almost80peopletookpart,manytravellinglargedistancestocome. TheworkshopwasorganisedaroundsixexpositorylecturesbyYairMinskyonthecombi- natorialpartofhisprogrammetoextendhisresultsonThurston’sendinglaminationconjecture foroncepuncturedtoritogeneralsurfaces.Notlongaftertheworkshop,acompleteproofofthe conjecturewasannouncedbyBrock,CanaryandMinsky.Thisisundoubtedlyoneofthemost importantdevelopmentsinthesubjectinthelastdecade,pavingthewayforacompleteunder- standingoftheinternalgeometryofhyperbolic3-manifolds,andinvolvingdeepunderstanding of the fascinating links between this geometry and the combinatorics of the curve complex. Minsky’slectures,reproducedinthisvolume,giveaninvaluableoverview. Aswasclearfromthetalksattheconference,hyperbolicgeometryiscurrentlydeveloping withastonishingrapidity.Wehopethattheexpositionsherewillprovideausefulguide.The volume is divided into three parts. Part I contains Minsky’s lectures together with other arti- cles on the geometry of hyperbolic 3-manifolds. The paper by Hodgson and Kerckhoff is an expositionoftheirrecentworkonconemanifolds.Thisiskeytomanyrecentdevelopments, in particular Brock and Bromberg’s proof, outlined here, of the long standing Bers’ density conjectureforincompressibleends.Otal’sresultonunknottednessisanimportantingredient. Other exciting developments concern the extension of known results from incompressible to compressibleboundaries,basedonarecentbreakthroughbyKleineidamandSoutowhohere explainanddevelopsomeoftheiradvances. PartIIrevolvesaroundseveralarticleswhichrevisitTroelsJørgensen’sfamousbuthitherto unpublishedpaperOnpairsofonce-puncturedtori.WearedelightedtohaveJørgensen’sper- missiontoincludehispaperhere.PartIIIcontainsthreeexpositorypapersoncloselyrelated topics,notablyEpstein,MardenandMarkovic’scounterexampletoThurston’sK=2conjec- ture. WewouldliketothanktheLondonMathematicalSocietyforfundingtheconference.The organiserswerethefirstandlasteditors,MakotoSakumaandYoungEunChoi.Theeditorsowe aconsiderabledebttoDavidSanderswhoseTEXpertiserapidlygotthearticlesforthisvolume intotheirpresentcoherentshape.WewouldalsoliketothankNicholasWickensforassisting withtheeditorialworkandYasushiYamashitaforputtingJørgensen’sarticleintoTEX. Finally,itwillnothaveescapednoticethatourconferencebeganonSeptember11,2001.In- evitablytheterribleeventsofthatdayovershadowedtheconferenceandoccupiedthethoughts ofalltheparticipants.Wewereverythankfulthateveryonearrivedsafelyandtheconference wasabletoproceedasplanned. YoheiKomori,VladimirMarkovicandCarolineSeries MathematicsInstitute,UniversityofWarwick,February2003 vii
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