A simple criterion for non-relative hyperbolicity and one-endedness of groups

Details A simple criterion for non-relative hyperbolicity and one-endedness of groups A simple criterion for non-relative hyperbolicity and one-endedness of groups

2005-04-13

arxiv.org/abs/math/0504271v3

Mathematics

Geometric Topology

13 pages, no figures. Argument generalised to cover a wider class of groups and to deduce their one-endedness

Scientific paper

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.

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