Séminaire Géométrie et groupes discrets
# Subgroups of Hyperbolic Groups, Finiteness Properties and Complex Hyperbolic Lattices

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Amphithéâtre Léon Motchane (IHES)
### Amphithéâtre Léon Motchane

#### IHES

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

Description

Following C.T.C. Wall, we say that a group G is of type F_{n} 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 F_{m-1} but not of type F_{m}. 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.

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Fanny Kassel

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