The geometry and topology of three-manifolds. voume IV

William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume IV contains Thurston's highly influential, though previously unpublished, 1977–78 Princeton Course Notes on the Geometry and Topology of 3-manifolds. It is an indispensable part of the Thurston collection but can also be used on its own as a textbook or for self-study. Cover 1/2 title Title page Copyright page Contents Publisher’s note Editor’s preface Introduction Geometry and three-manifolds Elliptic and hyperbolic geometry Geometric structures on manifolds Hyperbolic Dehn surgery Flexibility and rigidity of geometric structures Gromov’s invariant and the volume of a hyperbolic manifold Computation of volume Kleinian groups Algebraic convergence Note Deforming Kleinian manifolds by homeomorphisms of the sphere at infinity Orbifolds Index Other titles in this series Back Cover This set contains the Collected Works of William P. Thurston with Commentary, Volumes I-III, and The Geometry and Topology of Three-Manifolds. William Thurston's work connected whole mathematical subjects in entirely new ways and changed the way mathematicians think.