Limits of Baumslag-Solitar groups and dimension estimates in the space of marked groups
arXiv:1001.5371 · doi:10.4171/GGD/165
Abstract
We prove that the limits of Baumslag-Solitar groups which we previously studied are non-linear hopfian C*-simple groups with infinitely many twisted conjugacy classes. We exhibit infinite presentations for these groups, classify them up to group isomorphism, describe their automorphisms and discuss the word and conjugacy problems. Finally, we prove that the set of these groups has non-zero Hausforff dimension in the space of marked groups on two generators.
30 pages, no figures, english
References in corpus (5)
- C-simple groups: amalgamated free products, HNN extensions, and fundamental groups of 3-manifolds
- Spaces of closed subgroups of locally compact groups
- A sofic group away from amenable groups
- On the Structure of Some Reduced Amalgamated Free Product C*-Algebras
- Twisted conjugacy classes in nilpotent groups