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Finiteness properties of subgroups of hyperbolic groups

Claudio Llosa Isenrich (KIT)


11.05.2022 von 16:15 bis 17:45 (Europe/Berlin / UTC200)

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Hyperbolic groups form an important class of finitely presented groups. They are known to be of type Fn for all n, that is, they admit a classifying space with finitely many cells in all dimensions. It is natural to ask if subgroups of hyperbolic groups inherit these strong finiteness properties: For n ≥ 1, is there a subgroup of a hyperbolic group of type Fn, but not of type Fn+1? Brady raised this question in 1999, following his construction of examples for n=2, while the first examples for n=1 were constructed by Rips in 1982. Very recently Martelli, Py and myself constructed examples for n=3, while the question for n ≥ 4 remained open. In this talk I will explain how one can apply methods from complex geometry to uniform arithmetic lattices in SU(n,1) to answer Brady's question for all n. This is joint work with Py.