LEADER 03341nam 22004575a 450 001 9910151929703321 005 20100929234500.0 010 $a3-03719-582-7 024 70$a10.4171/082 035 $a(CKB)3710000000953861 035 $a(CH-001817-3)122-100929 035 $a(PPN)178155837 035 $a(EXLCZ)993710000000953861 100 $a20100929j20100929 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometrisation of 3-Manifolds$b[electronic resource] /$fLaurent Bessie?res, Ge?rard Besson, Michel Boileau, Sylvain Maillot, Joan Porti 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2010 215 $a1 online resource (247 pages) 225 0 $aEMS Tracts in Mathematics (ETM)$v13 330 $aThe Geometrisation Conjecture was proposed by William Thurston in the mid 1970s in order to classify compact 3-manifolds by means of a canonical decomposition along essential, embedded surfaces into pieces that possess geometric structures. It contains the famous Poincare? Conjecture as a special case. In 2002, Grigory Perelman announced a proof of the Geometrisation Conjecture based on Richard Hamilton's Ricci flow approach, and presented it in a series of three celebrated arXiv preprints. Since then there has been an ongoing effort to understand Perelman's work by giving more detailed and accessible presentations of his ideas or alternative arguments for various parts of the proof. This book is a contribution to this endeavour. Its two main innovations are first a simplified version of Perelman's Ricci flow with surgery, which is called Ricci flow with bubbling-off, and secondly a completely different and original approach to the last step of the proof. In addition, special effort has been made to simplify and streamline the overall structure of the argument, and make the various parts independent of one another. A complete proof of the Geometrisation Conjecture is given, modulo pre-Perelman results on Ricci flow, Perelman's results on the ?-functional and ?-solutions, as well as the Colding-Minicozzi extinction paper. The book can be read by anyone already familiar with these results, or willing to accept them as black boxes. The structure of the proof is presented in a lengthy introduction, which does not require knowledge of geometric analysis. The bulk of the proof is the existence theorem for Ricci flow with bubbling-off, which is treated in parts I and II. Part III deals with the long time behaviour of Ricci flow with bubbling-off. Part IV finishes the proof of the Geometrisation Conjecture. 606 $aDifferential & Riemannian geometry$2bicssc 606 $aManifolds and cell complexes$2msc 606 $aDifferential geometry$2msc 615 07$aDifferential & Riemannian geometry 615 07$aManifolds and cell complexes 615 07$aDifferential geometry 686 $a57-xx$a53-xx$2msc 700 $aBessie?res$b Laurent$01070605 702 $aBesson$b Ge?rard 702 $aBoileau$b Michel 702 $aMaillot$b Sylvain 702 $aPorti$b Joan 801 0$bch0018173 906 $aBOOK 912 $a9910151929703321 996 $aGeometrisation of 3-Manifolds$92564452 997 $aUNINA