A simple criterion for non-relative hyperbolicity and one-endedness of groups
arXiv:math/0504271
Abstract
We give a combinatorial criterion that implies both the non-strong relative hyperbolicity and the one-endedness of a finitely generated group. We use this to show that many important classes of groups do not admit a strong relatively hyperbolic group structure and have one end. Applications include surface mapping class groups, the Torelli group, (special) automorphism and outer automorphism groups of most free groups, and the three-dimensional Heisenberg group. Our final application is to Thompson's group F.
13 pages, no figures. Argument generalised to cover a wider class of groups and to deduce their one-endedness