Graphs of hyperbolic groups and a limit set intersection theorem

Sardar, Pranab

doi:10.1090/proc/13871

Graphs of hyperbolic groups and a limit set intersection theorem
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by Pranab Sardar PDF

Proc. Amer. Math. Soc. 146 (2018), 1859-1871 Request permission

Corrigendum: Proc. Amer. Math. Soc. 150 (2022), 2271-2276.

Abstract:

We define the notion of limit set intersection property for a collection of subgroups of a hyperbolic group; namely, for a hyperbolic group $G$ and a collection of subgroups $\mathcal S$ we say that $\mathcal S$ satisfies the limit set intersection property if for all $H,K \in \mathcal S$ we have $\Lambda (H)\cap \Lambda (K)=\Lambda (H\cap K)$. Given a hyperbolic group admitting a decomposition into a finite graph of hyperbolic groups structure with QI embedded condition, we show that the set of conjugates of all the vertex and edge groups satisfies the limit set intersection property.

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