Hyperbolic groups with spheres as boundary

Wolfgang Lueck (Hausdorff Research Institute for Mathematics and Rheinische Friedrich-Wilhelms-Universitae)

Abstract: Let G be a torsion-free hyperbolic group. Gromov made the conjecture that G is the fundamental group of a closed aspherical manifold if the boundary of G is homeomorphic to an (n-1)-dimensional sphere. After an introduction to hyperbolic groups, we will outline the ideas of the proof in dimension greater or equal to six by Bartels-Lueck-Weinberger.