Yves Stalder

Proper actions of wreath products and generalizations

We study stability properties of the Haagerup property and of coarse embeddability in a Hilbert space, under certain semidirect products. In particular, we prove that they are stable under taking standard wreath products. Our construction also allows for a characterization of subsets with relative Property T in a standard wreath product.

Highly transitive actions of free products

We characterize free products admitting a faithful and highly transitive action. In particular, we show that the group PS_2(Z) (isomorphic to the free product (Z/2Z) *(Z/3Z)) admits a faithful and highly transitive action on a countable set.

Limits of Baumslag–Solitar groups

We give a parametrization by

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

m

Proper actions of lamplighter groups associated with free groups

-adic integers of the limits of Baumslag-Solitar groups (marked with a canonical set of generators). It is shown to be continuous and injective on the invertible

Moyennabilité intérieure et extensions HNN

m

Wreath products with the integers, proper actions and Hilbert space compression

-adic integers. We show that all such limits are extensions of a free group by a lamplighter group and all but possibly one are not finitely presented. Finally, we give presentations related to natural actions on trees.

Convergence of Baumslag-Solitar groups

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.