The Geometrization Conjecture (Clay Mathematics Monographs, 5, Band 5)

Provides a complete proof of the geometrization conjecture, which describes all compact 3-manifolds in terms of geometric pieces. The method is to understand the limits as time goes to infinity of Ricci flow with surgery. The first half of the book is devoted to showing that these limits divide naturally along incompressible tori into pieces on which the metric is converging smoothly to hyperbolic metrics and pieces that are locally more and more volume collapsed. The second half of the book is devoted to showing that the latter pieces are themselves geometric.