A sofic group away from amenable groups
We give an example of a sofic group, which is not a limit of amenable groups.
math.GR↗
arXiv subjects
Yves Cornulier
Publications and source records attributed to Yves Cornulier.
Metabelian groups with quadratic Dehn function and Baumslag-Solitar groups
We prove that groups in a certain class of metabelian locally compact groups, have quadratic Dehn function. As an application, we embed the solvable Baumslag-Solitar groups into finitely presented metabelian groups with quadratic Dehn function. Also, we prove that Baumslag's finitely presented metabelian groups, in which the lamplighter groups embed, have quadratic Dehn function.
math.GR↗
On the Chabauty space of locally compact abelian groups
This paper contains several results about the Chabauty space of a general locally compact abelian group. Notably, we determine its topological dimension, we characterize when it is totally disconnected or connected; we characterize isolated points.
math.GR↗
On Property (FA) for wreath products
We characterize permutational wreath products with Property (FA). For instance, the standard wreath product A wr B of two nontrivial countable groups A,B, has Property (FA) if and only if B has Property (FA) and A is a finitely generated group with finite abelianisation. We also prove an analogous result for hereditary Property (FA). On the other hand, we prove that many wreath products with hereditary Property (FA) are not quotients of finitely presented groups with the same property.
math.GR↗
Compactly presented groups
This survey purports to be an elementary introduction to compactly presented groups, which are the analogue of finitely presented groups in the broader realm of locally compact groups. In particular, compact presentation is interpreted as a coarse simple connectedness condition on the Cayley graph, and in particular is a quasi-isometry invariant. In the appendix, an example of a Lie group, not quasi-isometric to any homogeneous graph, is given; the short argument relies on results of Trofimov and Pansu, anterior to~1990.
math.GR↗
The Howe-Moore property for real and p-adic groups
We consider in this paper a relative version of the Howe-Moore Property, about vanishing at infinity of coefficients of unitary representations. We characterize this property in terms of ergodic measure-preserving actions. We also characterize, for linear Lie groups or p-adic Lie groups, the pairs with the relative Howe-Moore Property with respect to a closed, normal subgroup. This involves, in one direction, structural results on locally compact groups all of whose proper closed characteristic subgroups are compact, and, in the other direction, some results about the vanishing at infinity of oscillatory integrals.
math.FA↗
A characterization of relative Kazhdan Property T for semidirect products with abelian groups
Let A be a locally compact abelian group, and H a locally compact group acting on A. Let G=HA be the semidirect product. We prove that the pair (G,A) has Kazhdan's Property T if and only if the only countably approximable H-invariant mean on the Borel subsets of the Pontryagin dual of A, supported at the neighbourhood of the trivial character, is the Dirac measure.
math.GR↗
On the Cantor-Bendixson rank of metabelian groups
We study the Cantor-Bendixson rank of metabelian and virtually metabelian groups in the space of marked groups, and in particular, we exhibit a sequence (G_n) of 2-generated, finitely presented, virtually metabelian groups of Cantor-Bendixson rank omega^n.
math.GR↗
The space of finitely generated rings
The space of marked commutative rings on n given generators is a compact metrizable space. We compute the Cantor-Bendixson rank of any member of this space. For instance, the Cantor-Bendixson rank of the free commutative ring on n generators is omega^n, where omega is the smallest infinite ordinal. More generally, we work in the space of finitely generated modules over a given commutative ring.
math.AC↗
A spectral gap property for subgroups of finite covolume in Lie groups
Let G be a real Lie group and H a lattice or, more generally, a closed subgroup of finite covolume in G. We show that the unitary representation lambda_{G/H} of G on L^2(G/H) has a spectral gap, that is, the restriction of lambda_{G/H} to the orthogonal of the constants in L^2(G/H) does not have almost invariant vectors. This answers a question of G. Margulis. We give an application to the spectral geometry of locally symmetric Riemannian spaces of infinite volume.
math.GR↗