Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices

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• Pierre Py (Université de Strasbourg)
• Friday 10 March 2023, 13:45-14:45
• MR13.

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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 arithmetic lattice in the group PU(m,1) 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.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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