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On the Cantor-Bendixson rank of metabelian groups

Yves Cornulier — 2011

Annales de l’institut Fourier

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 $ω^{n}$ .

A spectral gap property for subgroups of finite covolume in Lie groups

Bachir Bekka; Yves Cornulier — 2010

Colloquium Mathematicae

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 $λ_{G / H}$ of G on L²(G/H) has a spectral gap, that is, the restriction of $λ_{G / H}$ to the orthogonal complement of the constants in L²(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.

Relative Kazhdan property

Yves de Cornulier — 2006

Annales scientifiques de l'École Normale Supérieure

Géométries modèles de dimension trois

Yves de Cornulier

Séminaire de théorie spectrale et géométrie

On expose une preuve détaillée de la classification par Thurston des huit géométries modèles de dimension trois.

Amenable hyperbolic groups

Pierre-Emmanuel Caprace; Yves de Cornulier; Nicolas Monod; Romain Tessera — 2015

Journal of the European Mathematical Society

We give a complete characterization of the locally compact groups that are non elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting automorphisms. We moreover give a description of all Gromov-hyperbolic locally compact groups with a cocompact amenable subgroup: modulo a compact normal subgroup, these turn out to be either rank one simple Lie groups, or automorphism groups of semiregular trees acting doubly...

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