Séminaire Géométrie et groupes discrets

Subgroups of Hyperbolic Groups, Finiteness Properties and Complex Hyperbolic Lattices

by Prof. Pierre Py (CNRS & Université de Strasbourg)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

Following C.T.C. Wall, we say that a group G is of type Fn if it admits a classifying space which is a CW complex with finite n-skeleton. For n = 2, one recovers the notion of being finitely presented. We prove that in a cocompact complex hyperbolic arithmetic lattice with positive first Betti number, deep enough finite index subgroups admit plenty of homomorphisms to Z with kernel of type Fm-1 but not of type Fm. This provides many non-hyperbolic finitely presented subgroups of hyperbolic groups and answers an old question of Brady. This is based on a joint work with C. Llosa Isenrich.

Organized by

Fanny Kassel