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- W4289743782 abstract "We generalize Gruber--Sisto's construction of the coned--off graph of a small cancellation group to build a partially ordered set $mathcal{TC}$ of cobounded actions of a given small cancellation group whose smallest element is the action on the Gruber--Sisto coned--off graph. In almost all cases $mathcal{TC}$ is incredibly rich: it has a largest element if and only if it has exactly 1 element, and given any two distinct comparable actions $[Gcurvearrowright X] preceq [Gcurvearrowright Y]$ in this poset, there is an embeddeding $iota:P(omega)tomathcal{TC}$ such that $iota(emptyset)=[Gcurvearrowright X]$ and $iota(mathbb N)=[Gcurvearrowright Y]$. We use this poset to prove that there are uncountably many quasi--isometry classes of finitely generated group which admit two cobounded acylindrical actions on hyperbolic spaces such that there is no action on a hyperbolic space which is larger than both." @default.
- W4289743782 created "2022-08-04" @default.
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- W4289743782 date "2018-07-27" @default.
- W4289743782 modified "2023-10-16" @default.
- W4289743782 title "Actions of small cancellation groups on hyperbolic spaces" @default.
- W4289743782 doi "https://doi.org/10.48550/arxiv.1807.10524" @default.
- W4289743782 hasPublicationYear "2018" @default.
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