Cahit Arf Lecture 2010 by John W. Morgan
John W. MorganStony Brook University, Simons Center for Geometry and Physics
The Topology of 3-Dimensional Manifolds
|Date:||December 9, 2010
Cahit Arf Auditorium
Poincaré launched the subject of 3-dimensional topology in 1904. At the end of a long treatise on 3-manifolds he asked what became known as the Poincaré Conjecture: Is every simply connected 3-manifold homeomorphic to the 3-sphere. This problem sparked a century of work on manifolds of dimensions 3 and higher, work that made topology one of the most dynamic and exciting areas of mathematics during the 20th century. But in spite of all this work, at the end of the 20th century the Poincaré Conjecture still stood unresolved. Then in 2002 and 2003, Grigory Perelman put a series of 3 preprints on the archive that completely resolved this conjecture and the more general conjecture, due to Thurston, about the structure of all 3-manifolds. His approach was to use work of Richard Hamilton concerning what is called the Ricci flow. This is a parabolic evolution equation for a Riemannian metric on a manifold. In this talk we will review the motivating questions and the Ricci flow. After giving this background we will then sketch Perelman’s method of solution.