Recent progress on the Poincare conjecture and the classification of 3-manifolds

Morgan, J

Table of contents :
Introduction……Page 1
1.2. Dimension 3……Page 3
2. Topology of 3-manifolds……Page 5
2.1. The Prime Decomposition……Page 6
2.2. Thurston’s Geometrization Conjecture……Page 7
3. Hamilton’s Ricci flow equation……Page 8
3.2. Relation of the Ricci Flow Equation to the Heat Equation……Page 9
3.3. Hamilton’s First Results……Page 10
4. Perelman’s claims……Page 11
4.2. Regions of High Curvature in the Flow……Page 12
4.3. Regions of High Curvature at the Singular Time……Page 13
4.5. The Collapsed Regions……Page 18
5. Concluding remarks……Page 20
References……Page 21