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arXiv · 2308.08353

Finiteness properties and Relatively Hyperbolic Groups

Harsh Patil
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Abstract

We show that properties $F_n$ and $FP_n$ hold for a relatively hyperbolic group if and only if they hold for all the peripheral subgroups. As an application we show that there are at least countably many distinct quasi-isometry classes of one-ended groups that are type $F_n$ but not $F_{n+1}$ and similarly of type $FP_n$ and not $FP_{n+1}$ for all positive integers $n$.

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Harsh Patil. 2023-08-16. Finiteness properties and Relatively Hyperbolic Groups. https://doi.org/10.1112/blms.70039

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