Geometric Structures on Manifolds

The study of locally homogeneous geometric structures on manifolds was initiated by Charles Ehresmann in 1936, who first proposed the classification of putting a “classical geometry” on a topological manifold. In the late 1970’s, locally homogeneous Riemannian structures on 3-manifolds formed the context for Bill Thurston’s Geometrization Conjecture, later proved by Perelman. This book develops the theory of geometric structures modeled on a homogeneous space of a Lie group, which are not necessarily Riemannian. Drawing on a diverse collection of techniques, we hope to invite researchers at all levels to this fascinating and currently extremely active area of mathematics.