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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
