Graphs of hyperbolic groups and a limit set intersection theorem

Pranab Sardar

Published 2016-06-23Version 1

We say that a collection $\mathcal S$ of subgroups of a hyperbolic group $G$ satisfies the limit set intersection property if for any $H, K\in \mathcal S$ we have $\Lambda(H)\cap \Lambda(K)=\Lambda(H\cap K)$. If a hyperbolic group $G$ admits a decomposition into a graph of hyperbolic groups with qi embedded condition then we show that the collection of conjugates of the vertex groups and the edge groups satisfy the limit set intersection property.