A hyperbolic group with a finitely presented subgroup that is not of type $FP_3$

preprint2014arXivOpen access

Brady proved that there are hyperbolic groups with finitely presented subgroups that are not of type $FP_3$ (and hence not hyperbolic). We reprove Brady's theorem by presenting a new construction. Our construction uses Bestvina-Brady Morse theory, but does not involve branched coverings.

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A hyperbolic group with a finitely presented subgroup that is not of type $FP_3$

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A hyperbolic group with a finitely presented subgroup that is not of type FP3FP_3FP3​

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A hyperbolic group with a finitely presented subgroup that is not of type $FP_3$