Subgroups of Hyperbolic Groups, Finiteness Properties and Complex Hyperbolic Lattices

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

lundi 16 janv. 2023, 16:00 → 17:15 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

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.