Hyperbolic structures on groups

  title={Hyperbolic structures on groups},
  author={Carolyn R. Abbott and Sahana Balasubramanya and Denis V. Osin},
  journal={Algebraic \& Geometric Topology},
For every group $G$, we introduce the set of hyperbolic structures on $G$, denoted $\mathcal{H}(G)$, which consists of equivalence classes of (possibly infinite) generating sets of $G$ such that the corresponding Cayley graph is hyperbolic; two generating sets of $G$ are equivalent if the corresponding word metrics on $G$ are bi-Lipschitz equivalent. Alternatively, one can define hyperbolic structures in terms of cobounded $G$-actions on hyperbolic spaces. We are especially interested in the… 
Actions of small cancellation groups on hyperbolic spaces
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A topological zero-one law and elementary equivalence of finitely generated groups
  • D. Osin
  • Mathematics
    Ann. Pure Appl. Log.
  • 2021
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