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Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices

Abstract : 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.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03667376
Contributor : Pierre Py Connect in order to contact the contributor
Submitted on : Friday, May 13, 2022 - 1:26:11 PM
Last modification on : Saturday, May 14, 2022 - 3:36:40 AM

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  • HAL Id : hal-03667376, version 1
  • ARXIV : 2204.05788

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Claudio Llosa Isenrich, Pierre Py. Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices. 2022. ⟨hal-03667376⟩

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