MARC Record from marc_columbia

LEADER: 03935cam a22003854a 4500
001 6296017
005 20221122020041.0
008 070530t20072007riua b 001 0 eng
010 $a 2007062016
015 $aGBA770992$2bnb
016 7 $a013833905$2Uk
020 $a9780821843284 (alk. paper)
020 $a0821843281 (alk. paper)
035 $a(OCoLC)ocn145147251
035 $a(OCoLC)145147251
035 $a(NNC)6296017
035 $a6296017
040 $aDLC$cDLC$dBAKER$dC#P$dYDXCP$dBTCTA$dUKM$dOrLoB-B
050 00 $aQA670$b.M67 2007
082 00 $a516.3/62$222
100 1 $aMorgan, John,$d1946 March 21-$0http://id.loc.gov/authorities/names/n2013067496
245 10 $aRicci flow and the Poincaré conjecture /$cJohn Morgan, Gang Tian.
260 $aProvidence, RI :$bAmerican Mathematical Society :$bClay Mathematics Institute,$c[2007], ©2007.
300 $axlii, 521 pages :$billustrations ;$c27 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aClay mathematics monographs,$x1539-6061 ;$vv. 3
504 $aIncludes bibliographical references (p. 515-518) and index.
505 00 $gPt. 1.$tBackground from Riemannian geometry and Ricci flow --$gCh. 1.$tPreliminaries from Riemannian geometry --$gCh. 2.$tManifolds of non-negative curvature --$gCh. 3.$tBasics of Ricci flow --$gCh. 4.$tThe maximum principle --$gCh. 5.$tConvergence results for Ricci flow --$gPt. 2.$tPerelman's length function and its applications --$gCh. 6.$tA comparison geometry approach to the Ricci flow --$gCh. 7.$tComplete Ricci flows of bounded curvature --$gCh. 8.$tNon-collapsed results --$gCh. 9.$t[kappa]-non-collapsed ancient solutions --$gCh. 10.$tBounded curvature at bounded distance --$gCh. 11.$tGeometric limits of generalized Ricci flows --$gCh. 12.$tThe standard solution --$gPt. 3.$tRicci flow with surgery --$gCh. 13.$tSurgery on a [delta]-neck --$gCh. 14.$tRicci flow with surgery : the definition --$gCh. 15.$tControlled Ricci flows with surgery --$gCh. 16.$tProof of non-collapsing --$gCh. 17.$tCompletion of the proof of Theorem 15.9 --$gPt. 4.$tCompletion of the proof of the Poincare conjecture --$gCh. 18.$tFinite-time extinction --$gCh. 19.$tCompletion of the proof of proposition 18.24 --$gApp.$t3-manifolds covered by canonical neighborhoods.
520 1 $a"This book provides full details of a complete proof of the Poincare Conjecture following Perelman's three preprints. After a lengthy introduction that outlines the entire argument, the book is divided into four parts. The first part reviews necessary results from Riemannian geometry and Ricci flow, including much of Hamilton's work. The second part starts with Perelman's length function, which is used to establish crucial non-collapsing theorems. Then it discusses the classification of non-collapsed, ancient solutions to the Ricci flow equation. The third part concerns the existence of Ricci flow with surgery for all positive time and an analysis of the topological and geometric changes introduced by surgery. The last part follows Perelman's third preprint to prove that when the initial Riemannian 3-manifold has finite fundamental group, Ricci flow with surgery becomes extinct after finite time. The proofs of the Poincare Conjecture and the closely related 3-dimensional spherical space-form conjecture are then immediate." "With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology."--BOOK JACKET.
650 0 $aRicci flow.$0http://id.loc.gov/authorities/subjects/sh2004000290
650 0 $aPoincaré conjecture.$0http://id.loc.gov/authorities/subjects/sh2007003945
700 1 $aTian, G.
830 0 $aClay mathematics monographs ;$vv. 3.$0http://id.loc.gov/authorities/names/n2003010518
852 00 $bmat$hQA670$i.M67 2007