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Relative hyperbolicity, trees of spaces and Cannon-Thurston maps

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Abstract

We prove the existence of continuous boundary extensions (Cannon-Thurston maps) for the inclusion of a vertex space into a tree of (strongly) relatively hyperbolic spaces satisfying the qi-embedded condition. This implies the same result for inclusion of vertex (or edge) subgroups in finite graphs of (strongly) relatively hyperbolic groups. This generalizes a result of Bowditch for punctured surfaces in 3 manifolds and a result of Mitra for trees of hyperbolic metric spaces.

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Authors and Affiliations

  1. RKM Vivekananda University, Belur Math, 711202, India

    Mahan Mj

  2. Stat-Math Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata, 700108, India

    Abhijit Pal

Authors
  1. Mahan Mj
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  2. Abhijit Pal
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Correspondence to Mahan Mj.

Additional information

This paper is part of AP’s Ph.D. thesis written under the supervision of MM.

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Mj, M., Pal, A. Relative hyperbolicity, trees of spaces and Cannon-Thurston maps. Geom Dedicata 151, 59–78 (2011). https://doi.org/10.1007/s10711-010-9519-2

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  • DOI: https://doi.org/10.1007/s10711-010-9519-2

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