Poincare conjecture or Hamilton-Perelman theorem
Dr. C.S. Aravinda
Chennai Mathematical Institute.
Trying to resolve the famous 1904 conjecture of Poincare that a closed, simply connected 3-manifold is homeomorphic to the unit 3-sphere dominated the field of Topology during 20th century. Its dramatic resolution by Perelman almost one hundred years later using the Ricci flow approach initiated by Hamilton in 1982 is as much a triumph for the Geometric analysis methods as for Mathematics itself. Could this remarkable achievement in the early years of this new millennium mark a new beginning in our understanding of the 3-dimensional manifold topology?
In the first of this two-part talk, I briefly trace various stages of this development leading to Hamilton's seminal paper of 1982 in the Journal of Differential Geometry. In the second part, I will sketch some of the crucial ideas in Perelman's work.