JournalsggdVol. 6, No. 3pp. 533–577

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

  • Luc Guyot

    Universität Göttingen, Germany
  • Yves Stalder

    Université Blaise Pascal, Aubière, France
Limits of Baumslag–Solitar groups and dimension estimates in the space of marked groups cover
Download PDF

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.

Cite this article

Luc Guyot, Yves Stalder, Limits of Baumslag–Solitar groups and dimension estimates in the space of marked groups. Groups Geom. Dyn. 6 (2012), no. 3, pp. 533–577

DOI 10.4171/GGD/165