James W. Anderson, Javier Aramayona, Kenneth J. Shackleton
Published 2005-04-13, updated 2005-11-23Version 3
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.
Comments: 13 pages, no figures. Argument generalised to cover a wider class of groups and to deduce their one-endedness
On endomorphisms of surface mapping class groups
Braid groups and Iwahori-Hecke algebras
The topology of 3-manifolds, Heegaard distance and the mapping class group of a 2-manifold
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