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Graphs of hyperbolic groups and a limit set intersection theorem


Author: Pranab Sardar
Journal: Proc. Amer. Math. Soc. 146 (2018), 1859-1871
MSC (2010): Primary 20F67
DOI: https://doi.org/10.1090/proc/13871
Published electronically: December 26, 2017
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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

DOI: https://doi.org/10.1090/proc/13871
Keywords: Hyperbolic groups, limit sets, Bass-Serre theory
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
Article copyright: © Copyright 2017 American Mathematical Society

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