3-manifolds everywhere

2014/04/28 by Danny Calegari, Calegari, Danny, Henry Wilton +1
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.1404.7043

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

arxiv created 2017/02/21 · arxiv updated 2017/02/23

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).

Related

• Coxeter groups and random groups
• Uniform models and short curves for random 3-manifolds
• Random extensions of free groups and surface groups are hyperbolic
• Quasi-isometric rigidity of three manifold groups
• Determining subgroups via stationary measures