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## Abstract

We investigate groups whose Cayley graphs have poorly connected subgraphs. We prove that a ﬁnitely generated group has bounded separation in the sense of Benjamini–Schramm–Tim´ar if and only if it is virtually free. We then prove a gap theorem for connectivity of ﬁnitely presented groups, and prove that there is no comparable theorem for all ﬁnitely generated groups. Finally, we formulate a connectivity version of the conjecture that every group of type F with no Baumslag-Solitar subgroup is hyperbolic, and prove it for groups with at most quadratic Dehn function.

Original language | English |
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Pages (from-to) | 4653-4664 |

Journal | Proceedings of the American Mathematical Society |

Volume | 148 (2020) |

DOIs | |

Publication status | Published - 14 Aug 2020 |

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Dive into the research topics of 'Poorly connected groups'. Together they form a unique fingerprint.## Projects

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