Thomas Delzant

Cuts in Kähler Groups

We study fundamental groups of Kahler manifolds via their cuts or relative ends. Mathematics Subject Classification (2000). 32Q15, 20F65, 57M07.

Kahler groups, real hyperbolic spaces and the Cremona group. With an appendix by S. Cantat.

Generalizing a classical theorem of Carlson and Toledo, we prove that any Zariski dense isometric action of a Kahler group on the real hyperbolic space of dimension at least 3 factors through a homomorphism onto a cocompact discrete subgroup of PSL2(R). We also study actions of Kahler groups on infinite dimensional real hyper- bolic spaces, describe some exotic actions of PSL2(R) on these spaces, and give an application to the study of the Cremona group.

Accessibilité hiérarchique des groupes de présentation finie

Abstract We prove that a finitely presented group admits a finite hierarchy obtained by successive splittings along a family of elementary subgroups.

Sur l'accessibilité acylindrique des groupes de présentation finie

Soient G un groupe, et τ un G-arbre, c’est-a-dire un arbre muni d’une action de G sans inversion d’aretes. Le probleme d’accessibilite est celui de donner une borne a priori au nombre de sommets de τ/G. Ce probleme a ete etudie par de nombreux auteurs : outre le celebre theoreme de Grushko sur les produit libres, citons les travaux de M. Dunwoody [Du], M. Bestvina et M. Feighn [BF], Z. Sela [S] et l’auteur [De1], [DP].

Codimension one subgroups and boundaries of hyperbolic groups

We construct hyperbolic groups with the following properties: The boundary of the group has big dimension, it is separated by a Cantor set and the group does not split. This shows that Bowditchs theorem that characterizes splittings of hyperbolic groups over 2-ended groups in terms of the boundary can not be extended to splittings over more complicated subgroups.

Homomorphic Images of Branch Groups, and Serre’s Property (FA)

It is shown that a finitely generated branch group has Serre’s property (FA) if and only if it does not surject onto the infinite cyclic group or the infinite dihedral group. An example of a finitely generated self-similar branch group surjecting onto the infinite cyclic group is constructed.