Geometric structures on 3-manifolds

Abstract

Three-dimensional manifolds are of central importance in topology, algebra, and cosmology (providing models for the universe). Thurston's Geometrization Conjecture gives a beautiful conjectural picture of 3-manifolds in terms of eight uniform geometries, but the conjecture and some of its basic consequences remain unproved. This project is aimed at making advances on fundamental questions in the following areas: * construction of geometric structures by deformation methods, * computation of geometric structures, * geometric and algebraic invariants.