Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866907769629573120 |
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| author | Isenrich, Claudio Llosa Py, Pierre |
| author_facet | Isenrich, Claudio Llosa Py, Pierre |
| contents | We prove that in a cocompact complex hyperbolic arithmetic lattice $Γ< {\rm PU}(m,1)$ 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 Kähler manifolds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2204_05788 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices Isenrich, Claudio Llosa Py, Pierre Group Theory Complex Variables Differential Geometry Geometric Topology 20F67 (Primary) 20F65, 20J05, 32J27, 57M07 (Secondary) We prove that in a cocompact complex hyperbolic arithmetic lattice $Γ< {\rm PU}(m,1)$ 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 Kähler manifolds. |
| title | Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices |
| topic | Group Theory Complex Variables Differential Geometry Geometric Topology 20F67 (Primary) 20F65, 20J05, 32J27, 57M07 (Secondary) |
| url | https://arxiv.org/abs/2204.05788 |