Related papers: Neretin groups admit no non-trivial invariant rand…

We construct locally compact groups with no non-trivial Invariant Random Subgroups and no non-trivial Uniformly Recurrent Subgroups.

We present a contribution to the structure theory of locally compact groups. The emphasis is on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic…

We show that the left regular representation of Neretin groups is factorial, providing the first example of a non-discrete simple group with this property. This is based on a new criterion of factoriality for totally disconnected groups.…

This is the extended version of the talk we gave during the Arbeitsgemeinschaft on totally disconnected locally compact groups, held in Oberwolfach in October 2014. We give the definition of the Neretin group of spheromorphisms of the…

The Neretin group $\mathcal{N}_{d,k}$ is the totally disconnected locally compact group consisting of almost automorphisms of the tree $\mathcal{T}_{d,k}$. This group has a distinguished open subgroup $\mathcal{O}_{d,k}$. We prove that this…

We prove that a finitely generated group contains a sequence of non-trivial elements which converge to the identity in every compact homomorphic image if and only if the group is not virtually abelian.

We show that any group $G$ is contained in some sharply 2-transitive group $\mathcal{G}$ without a non-trivial abelian normal subgroup. This answers a long-standing open question. The involutions in the groups $\mathcal{G}$ that we…

A number of properties of spherical Artin groups extend to Garside groups, defined as the groups of fractions of monoids where least common multiples exist, there is no nontrivial unit, and some additional finiteness conditions are…

We study when a piecewise full group (a.k.a. topological full group) of homeomorphisms of the Cantor space $X$ can be given a non-discrete totally disconnected locally compact (t.d.l.c.) topology and give a criterion for the alternating…

A closed subgroup $H$ of a locally compact group $G$ is confined if the closure of the conjugacy class of $H$ in the Chabauty space of $G$ does not contain the trivial subgroup. We establish a dynamical criterion on the action of a totally…

We show that the group of almost automorphisms of a d-regular tree does not admit lattices. As far as we know this is the first such example among (compactly generated) simple locally compact groups.

Let G be a finite group. A collection P={H1, ..., Hr} of subgroups of G, where r > 1, is said a non-trivial partition of G if every non-identity element of G belongs to one and only one Hi, for some 1 <=i<=r. We call a group G that does not…

Wreath products of non-discrete locally compact groups are usually not locally compact groups, nor even topological groups. We introduce a natural extension of the wreath product construction to the setting of locally compact groups. As an…

We construct examples of non-bi-orderable one-relator groups without generalized torsion. This answers a question asked in [2].

This article resolves several long-standing conjectures about Artin groups of euclidean type. In particular, we prove that every irreducible euclidean Artin group is a torsion-free centerless group with a decidable word problem and a…

We consider group orders and right-orders which are discrete, meaning there is a least element which is greater than the identity. We note that free groups cannot be given discrete orders, although they do have right-orders which are…

We construct the first sharply $3$-transitive groups not arising from a near field, i.e. point stabilizers have no nontrivial abelian normal subgroup.

We prove that nonvanishing of the first Novikov-Betti number implies that the fundamental group contains a nonabelian free subgroup.

We reduce a strong version of the twist conjecture for Artin groups to Artin groups whose defining graphs have no separating vertices. This produces new examples of Artin groups satisfying the conjecture, and sheds more light on the…

We exhibit abelian topological groups admitting no nontrivial strongly continuous irreducible representations in Banach spaces. Among them are some abelian Banach-Lie groups and some monothetic subgroups of the unitary group of a separable…