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1、AnintroductiontoHamiltonandPerelman’sworkontheconjecturesofPoincar´eandThurstonNotesoftheTalksgivenbyAlexanderBorisenkoinValencia,May-August2004writtenbyAlexanderBorisenkoGeometryDepartment.Math.-Mech.Faculty.KharkovNationalUniversity.Pl.Svobodu4,61007-Kharkov.Ukraine,EstherC
2、abezasandVicenteMiquelDepartamentdeGeometriaiTopologia.UniversitatdeValencia.46100-Burjassot(Valencia)SpainAcknowledgmentsA.Borisenkowassupportedbyagrant“Estadestemporalsperaprofessorscon-vidats(2003)”oftheUniversityofValencia.HealsothankstheDepartmentofGeometryandTopologyoft
3、hisUniversitybytheenvironment,thebibliograph-icalandtechnicalmeans,andthepossibilityofgivingthesetalks.E.CabezaswassupportedbyaGrantoftheProgramaNacionaldeFormaci´ondelProfesoradoUniversitarioref:APE2003-3344V.MiquelwaspartiallysupportedbyDGI(Spain)andFEDERProjectMTM2004-0601
4、5-C02-01,byAVCiTGRUPOS03/169,andwasinsabbaticalyearfromtheUniversityofValenciaalongabigpartoftetimewhenthesenoteswerewritten.PREFACEThesenotescontainthelecturesgivenbyA.BorisenkoinaSeminaronthePerelman’sworkonconjecturesofPoincar´eandThurstonheldintheDepartmentofGeometryandTo
5、pologyoftheUniversityofValenciaalongthemonthsofMay,June,JulyandAugust2004,.Thewrittenlecturescorrespondtothe“spoken”onesonlyinabroadsense.Sometimes,theorderofthelectureshasbeenchangedfollowingtheconvenienceofthewriters.ThelectureswerefirstwrittenbyA.Borisenkowhenpreparinghista
6、lks.Basedonthesenotesandthelectures,andwiththereferencesathand,12A.BORISENKO,E.CABEZAS-RIVAS,V.MIQUEL-MOLINAE.CabezasandV.Miquelwroteafirstversion.Thiswascorrectedbythespeaker,thenthesecondandthirdauthormodifiedthefirstversion,and,then,newcorrectionsandwritingsuntiltheauthorsarr
7、ivedtoanagreement.Wethinkitisimpossibletogiveacompleteaccountofthetopicsofthesenotesinonly140pages.Thepaperisdirectedtolaypeopleinthemainsubjectofit(Ricciflow)andalsothetopologicalbackgroundoftheproblem.Then,thegeneralphilosophyofthemistobeginwiththemoreelementaryfacts,givesom
8、edetailsonthem(sometimesmanydetails),andintroducetothemoreadvancedto
