The Poincaré conjecture : Clay Mathematics Institute Research Conference, resolution of the Poincaré conjecture, Institute Henri Poincaré, Paris, France, June 8-9, 2010

The conference to celebrate the resolution of the Poincaré conjecture, which is one of the Clay Mathematics Institute's seven Millennium Prize Problems, was held at the Institut Henri Poincaré in Paris. Several leading mathematicians gave lectures providing an overview of the conjecture--its history, its influence on the development of mathematics, and, finally, its proof. This volume contains papers based on the lectures at that conference. Taken together, they form an extraordinary record of the work that went into the solution of one of the great problems of mathematics. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA) Geometry In 2, 3 And 4 Dimensions / Michael Atiyah -- Years Of Topology : Work Stimulated By Poincare's Approach To Classifying Manifolds / John Morgan -- The Evolution Of Geometric Structures On 3-manifolds / Curtis Mcmullen -- Invariants Of Manifolds And The Classication Problem / Simon Donaldson -- Volumes Of Hyperbolic 3-manifolds / David Gabai -- Manifolds : Where Do We Come From? What Are We? Where Are We Going? / Mikhail Gromov -- Geometric Analysis On 4-manifolds / Gang Tian. James Carlson, Editor. Includes Bibliographical References. Content: Geometry in 2, 3 and 4 dimensions by M. Atiyah 100 Years of Topology: Work Stimulated by Poincare's Approach to Classifying Manifolds by J. Morgan The Evolution of Geometric Structures on 3-Manifolds by C. T. McMullen Invariants of Manifolds and the Classification Problem by S. K. Donaldson Volumes of Hyperbolic 3-Manifolds by D. Gabai, R. Meyerhoff, and P. Milley Manifolds: Where do we come from? What are we? Where are we going? by M. Gromov Geometric Analysis on 4-Manifolds by G. Tian