The_Geometry_and_Topology_of_Three-Manifolds-Thurston.pdf

(43492 KB) Pobierz
100516272 UNPDF
WilliamP.Thurston
TheGeometryandTopologyofThree-Manifolds
Electronicversion1.1-March2002
http://www.msri.org/publications/books/gt3m/
Thisisanelectroniceditionofthe1980notesdistributedbyPrincetonUniversity.
ThetextwastypedinT E XbySheilaNewbery,whoalsoscannedthefigures.Typos
havebeencorrected(andprobablyothersintroduced),butotherwisenoattempthas
beenmadetoupdatethecontents.GenevieveWalshcompiledtheindex.
Numbersontherightmargincorrespondtotheoriginaledition’spagenumbers.
Thurston’sThree-DimensionalGeometryandTopology,Vol.1(PrincetonUniversity
Press,1997)isaconsiderableexpansionofthefirstfewchaptersofthesenotes.Later
chaptershavenotyetappearedinbookform.
PleasesendcorrectionstoSilvioLevyatlevy@msri.org.
Introduction
Thesenotes(throughp.9.80)arebasedonmycourseatPrincetonin1978–
79.LargeportionswerewrittenbyBillFloydandSteveKerckho.Chapter7,by
JohnMilnor,isbasedonalecturehegaveinmycourse;theghostwriterwasSteve
Kerckho.Thenotesareprojectedtocontinueatleastthroughthenextacademic
year.Theintentistodescribetheverystrongconnectionbetweengeometryandlow-
dimensionaltopologyinawaywhichwillbeusefulandaccessible(withsomeeort)
tograduatestudentsandmathematiciansworkinginrelatedfields,particularly3-
manifoldsandKleiniangroups.
Muchofthematerialortechniqueisnew,andmoreofitwasnewtome.As
aconsequence,IdidnotalwaysknowwhereIwasgoing,andthediscussionoften
tendstowanter.Thecountrysideisscenic,however,anditisfuntotramparoundif
youkeepyoureyesalertanddon’tgetlost.Thetendencytomeanderratherthanto
followthequickestlinearrouteisespeciallypronouncedinchapters8and9,where
Ionlygraduallysawtheusefulnessof“traintracks”andthevalueofmappingout
someglobalinformationaboutthestructureofthesetofsimplegeodesiconsurfaces.
Iwouldbegratefultohearanysuggestionsorcorrectionsfromreaders,since
changesarefairlyeasytomakeatthisstage.Inparticular,bibliographicalinforma-
tionismissinginmanyplaces,andIwouldliketosolicitreferences(perhapsinthe
formofpreprints)andhistoricalinformation.
Thurston—TheGeometryandTopologyof3-Manifolds
iii
Contents
Introduction iii
Chapter1.Geometryandthree-manifolds 1
Chapter2.Ellipticandhyperbolicgeometry 9
2.1.ThePoincar´ediskmodel. 10
2.2.Thesouthernhemisphere. 11
2.3.Theupperhalf-spacemodel. 12
2.4.Theprojectivemodel. 13
2.5.Thesphereofimaginaryradius. 16
2.6.Trigonometry. 17
Chapter3.Geometricstructuresonmanifolds 27
3.1.Ahyperbolicstructureonthefigure-eightknotcomplement. 29
3.2.Ahyperbolicmanifoldwithgeodesicboundary. 31
3.3.TheWhiteheadlinkcomplement. 32
3.4.TheBorromeanringscomplement. 33
3.5.Thedevelopingmap. 34
3.8.Horospheres. 38
3.9.Hyperbolicsurfacesobtainedfromidealtriangles. 40
3.10.Hyperbolicmanifoldsobtainedbygluingidealpolyhedra. 42
Chapter4.HyperbolicDehnsurgery 45
4.1.IdealtetrahedrainH 3 . 45
4.2.Gluingconsistencyconditions. 48
4.3.Hyperbolicstructureonthefigure-eightknotcomplement. 50
4.4.Thecompletionofhyperbolicthree-manifoldsobtainedfromideal
polyhedra. 54
4.5.ThegeneralizedDehnsurgeryinvariant. 56
4.6.Dehnsurgeryonthefigure-eightknot. 58
4.8.Degenerationofhyperbolicstructures. 61
4.10.Incompressiblesurfacesinthefigure-eightknotcomplement. 71
Thurston—TheGeometryandTopologyof3-Manifolds v

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika:

Zgłoś jeśli naruszono regulamin