## Graphs of hyperbolic groups and a limit set intersection theorem

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**146**(2018), 1859-1871 Request permission

## 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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## Additional Information

**Pranab Sardar**- Affiliation: Indian Institute of Science Education and Research Mohali, Knowledge City, Sector 81, SAS Nagar, Manauli P.O. 140306, India
- MR Author ID: 854800
- Received by editor(s): September 13, 2016
- Received by editor(s) in revised form: June 27, 2017
- Published electronically: December 26, 2017
- Communicated by: Ken Bromberg
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**146**(2018), 1859-1871 - MSC (2010): Primary 20F67
- DOI: https://doi.org/10.1090/proc/13871
- MathSciNet review: 3767341