Subgroups of Hyperbolic Groups, Finiteness Properties and Complex Hyperbolic Lattices

Explore a 42-minute lecture on subgroups of hyperbolic groups, finiteness properties, and complex hyperbolic lattices presented by Pierre Py at the Workshop on Geometry of Subgroups. Delve into the concept of groups of type F_n as defined by C.T.C. Wall, with a focus on finitely presented groups when n=2. Discover the speaker's findings on cocompact arithmetic lattices in PU(m,1) with positive first Betti number, revealing that deep enough finite index subgroups possess numerous homomorphisms to Z with kernels of type F_{m-1} but not F_m. Learn how this research provides examples of non-hyperbolic finitely presented subgroups within hyperbolic groups, addressing a longstanding question posed by Brady. Gain insights into this collaborative work with C. Llosa Isenrich, presented as part of the Centre de recherches mathématiques (CRM) workshop series.