{"product_id":"ricci-flow-and-the-poincare-conjecture-9781470473167","title":"Ricci Flow and the Poincare Conjecture","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eFor over 100 years the Poincare Conjecture, which proposes a topological characterization of the 3-sphere, has been the central question in topology. Since its formulation, it has been repeatedly attacked, without success, using various topological methods. Its importance and difficulty were highlighted when it was chosen as one of the Clay Mathematics Institute's seven Millennium Prize Problems. In 2002 and 2003 Grigory Perelman posted three preprints showing how to use geometric arguments, in particular the Ricci flow as introduced and studied by Hamilton, to establish the Poincare Conjecture in the affirmative.   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 le\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eThe comprehensive and carefully detailed nature of the text makes this book an invaluable resource for any mathematician who wants to understand the technical nuts and bolts of the proof, while the introductory chapter provides an excellent conceptual overview of the entire argument.\" —\u003ci\u003eMathematical Reviews \u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eBackground from Riemannian geometry and Ricci flow: Preliminaries from Riemannian geometry\u003c\/li\u003e\n\u003cli\u003eManifolds of non-negative curvature\u003c\/li\u003e\n\u003cli\u003eBasics of Ricci flow\u003c\/li\u003e\n\u003cli\u003eThe maximum principle\u003c\/li\u003e\n\u003cli\u003eConvergence results for Ricci flow\u003c\/li\u003e\n\u003cli\u003ePerelman's length function and its applications: A comparison geometry approach to the Ricci flow\u003c\/li\u003e\n\u003cli\u003eComplete Ricci flows of bounded curvature\u003c\/li\u003e\n\u003cli\u003eNon-collapsed results\u003c\/li\u003e\n\u003cli\u003e$\\kappa$-non-collapsed ancient solutions\u003c\/li\u003e\n\u003cli\u003eBounded curvature at bounded distance\u003c\/li\u003e\n\u003cli\u003eGeometric limits of generalized Ricci flows\u003c\/li\u003e\n\u003cli\u003eThe standard solution\u003c\/li\u003e\n\u003cli\u003eRicci flow with surgery: Surgery on a $\\delta$-neck\u003c\/li\u003e\n\u003cli\u003eRicci flow with surgery: The definition\u003c\/li\u003e\n\u003cli\u003eControlled Ricci flows with surgery\u003c\/li\u003e\n\u003cli\u003eProof of non-collapsing\u003c\/li\u003e\n\u003cli\u003eCompletion of the proof of Theorem 15.9\u003c\/li\u003e\n\u003cli\u003eCompletion of the proof of the Poincare conjecture: Finite-time extinction\u003c\/li\u003e\n\u003cli\u003eCompletion of the proof of Proposition 18.24\u003c\/li\u003e\n\u003cli\u003e3-manifolds covered by canonical neighborhoods\u003c\/li\u003e\n\u003cli\u003eBibliography\u003c\/li\u003e\n\u003cli\u003eIndex\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":51863303848279,"sku":"9781470473167","price":63.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470473167.jpg?v=1759920231","url":"https:\/\/bookcurl.com\/products\/ricci-flow-and-the-poincare-conjecture-9781470473167","provider":"Book Curl","version":"1.0","type":"link"}