اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدActions of small cancellation groups on hyperbolic spaces
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We generalize Gruber--Sistos 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.
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