Teichmüller Theory and Applications to Geometry, Topology, and Dynamics
Abstract
This volume is the second of four volumes devoted to Teichmüller theory and its applications to geometry, topology, and dynamics. The first volume gave an introduction to Teichmüller theory.
Volumes 2 through 4 prove four theorems by William Thurston:
The classification of homeomorphisms of surfaces
The topological characterization of rational maps
The hyperbolization theorem for 3-manifolds that fiber over the circle
The hyperbolization theorem for Haken 3-manifolds
These theorems are of extraordinary beauty in themselves, and the methods Thurston used to prove them were so novel and displayed such amazing
geometric insight that to this day they have barely entered the accepted methods of mathematicians in the field [...]