Geodesic
Limits of Baumslag–Solitar groups and dimension estimates in the space of marked groups
Luc Guyot1 ; Yves Stalder2
1Universität Göttingen, Germany
2Université Blaise Pascal, Aubière, France
Groups, geometry, and dynamics, Tome 6 (2012) no. 3, pp. 533-577

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DOI

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.
DOI : 10.4171/ggd/165
Classification : 20-XX, 00-XX
Mots-clés : Baumslag–Solitar groups, space of marked groups, Turing degree, Hausdorff dimension

Luc Guyot  1   ; Yves Stalder  2

1 Universität Göttingen, Germany
2 Université Blaise Pascal, Aubière, France 
Luc Guyot; Yves Stalder. Limits of Baumslag–Solitar groups and dimension estimates in the space of marked groups. Groups, geometry, and dynamics, Tome 6 (2012) no. 3, pp. 533-577. doi: 10.4171/ggd/165
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     year = {2012},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/165/}
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