3-manifolds everywhere

Abstract

A random group contains many subgroups which are isomorphic to the fundamental group of a compact hyperbolic 3-manifold with totally geodesic boundary. These subgroups can be taken to be quasi-isometrically embedded. This is true both in the few relators model, and the density model of random groups (at any density less than a half).

38 pages, 10 figures; v2: typos corrected; v3: this is the final version accepted for publication