Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices

Claudio Llosa Isenrich; Pierre Py

doi:10.1007/s00222-023-01223-3

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arXiv · 2204.05788

Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices

Claudio Llosa Isenrich·Pierre Py

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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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BibTeX RIS

Claudio Llosa Isenrich, Pierre Py. 2022-04-12. Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices. https://doi.org/10.1007/s00222-023-01223-3

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