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76,95 €Preface v
Press Release vii
Permissions and Acknowledgments xvii
• Geometry in 2, 3 and 4 Dimensions
Michael Atiyah 1
• 100 Years of Topology: Work Stimulated by Poincar´e’s Approach to Classifying Manifolds
John W. Morgan 7
• The Evolution of Geometric Structures on 3-Manifolds
Curtis T. McMullen 31
• Invariants of Manifolds and the Classification Problem
Simon K. Donaldson 47
• Volumes of Hyperbolic 3-Manifolds
David Gabai, Robert Meyerhoff, and Peter Milley 65
• Manifolds: Where do we come from? What are we? Where are we going?
Mikhail Gromov 81
• Geometric Analysis on 4-Manifolds
Gang Tian 145
A co-publication of the AMS and Clay Mathematics Institute
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.
Author
James Carlson: Clay Mathematics Institute, Cambridge, MA
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