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Article Dans Une Revue Inventiones Mathematicae Année : 2024

Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices

Résumé

We prove that in a cocompact complex hyperbolic arithmetic lattice $\Gamma < {\rm PU}(m,1)$ of the simplest type, deep enough finite index subgroups admit plenty of homomorphisms to $\mathbb{Z}$ with kernel of type $\mathscr{F}_{m-1}$ but not of type $\mathscr{F}_{m}$. This provides many finitely presented non-hyperbolic subgroups of hyperbolic groups and answers an old question of Brady. Our method also yields a proof of a special case of Singer's conjecture for aspherical K\"ahler manifolds.

Dates et versions

hal-03667376 , version 1 (13-05-2022)

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Claudio Llosa Isenrich, Pierre Py. Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices. Inventiones Mathematicae, 2024, 235 (1), pp.233-254. ⟨10.1007/s00222-023-01223-3⟩. ⟨hal-03667376⟩
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