Limits of Baumslag–Solitar groups and dimension estimates in the space of marked groups

Abstract

We prove that the limits of Baumslag–Solitar groups studied by the authors 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 Hausdorff dimension in the space of marked groups on two generators.