A limit set intersection theorem for graphs of relatively hyperbolic groups

Abstract

Let G be a relatively hyperbolic group that admits a decomposition into a finite graph of relatively hyperbolic groups structure with quasi-isometrically (qi) embedded condition. We prove that the set of conjugates of all the vertex and edge groups satisfy the limit set intersection property for conical limit points (refer to Definition 3 and Definition 23 for the definitions of conical limit points and limit set intersection property respectively). This result is motivated by the work of Sardar for graph of hyperbolic groups [16].

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Acknowledgements

The author is extremely grateful to Dr. Pranab Sardar for not only suggesting the problem but also for his invaluable comments, discussions and corrections. The author would like to thank Dr. Sushil Bhunia for proofreading the paper. The author would also like to thank the referee for the helpful suggestions and comments that improved the readability of the paper. Finally, the author would like to thank IISER, Mohali for the financial support towards this work.

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Correspondence to Swathi Krishna.

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Communicated by Mj Mahan.

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Krishna, S. A limit set intersection theorem for graphs of relatively hyperbolic groups. Proc Math Sci 130, 36 (2020). https://doi.org/10.1007/s12044-020-00563-x

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Keywords

  • Relatively hyperbolic groups
  • Cannon–Thurston maps
  • conical limit points
  • graph of groups

Mathematics Subject Classification

  • 20F65