Groups, Geometry, and Dynamics


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Volume 6, Issue 3, 2012, pp. 533–577
DOI: 10.4171/GGD/165

Published online: 2012-08-16

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

Luc Guyot[1] and Yves Stalder[2]

(1) Universität Göttingen, Germany
(2) Université Blaise Pascal, Aubière, France

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.

Keywords: Baumslag–Solitar groups, space of marked groups, Turing degree, Hausdorff dimension

Guyot Luc, Stalder Yves: Limits of Baumslag–Solitar groups and dimension estimates in the space of marked groups. Groups Geom. Dyn. 6 (2012), 533-577. doi: 10.4171/GGD/165