3-manifolds everywhere
Group Theory
2017-02-23 v3 Geometric Topology
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).
Cite
@article{arxiv.1404.7043,
title = {3-manifolds everywhere},
author = {Danny Calegari and Henry Wilton},
journal= {arXiv preprint arXiv:1404.7043},
year = {2017}
}
Comments
38 pages, 10 figures; v2: typos corrected; v3: this is the final version accepted for publication