The Geometrisation Conjecture was proposed by William Thurston in the mid 1970s in order to classify compact 3-manifolds by means of a canonical decomposition a
This book gives a complete proof of the geometrization conjecture, which describes all compact 3-manifolds in terms of geometric pieces, i.e., 3-manifolds with
For over 100 years the Poincare Conjecture, which proposes a topological characterization of the 3-sphere, has been the central question in topology. Since its
The field of 3-manifold topology has made great strides forward since 1982 when Thurston articulated his influential list of questions. Primary among these is P