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Relative hyperbolicity, trees of spaces and Cannon-Thurston maps. (English) Zbl 1222.57013
This paper proves a Cannon-Thurston map theorem for trees of relatively hyperbolic spaces. It generalizes previous Cannon-Thurston theorems of Bowditch and the first author.
The main theorem is stated in terms of trees of relatively hyperbolic spaces whose vertex spaces satisfy the quasi-isometrically embedded condition due to M. Bestvina and M. Feighn [J. Differ. Geom. 35, No. 1, 85–102 (1992; Zbl 0724.57029)]. Under some natural conditions of relative hyperbolicity, the inclusion of any vertex space in the tree of spaces has a Cannon-Thurston map, namely the embedding extends continuously to the boundary.
This is part of Pal’s PhD thesis supervised by Mj.

57M50 General geometric structures on low-dimensional manifolds
20F65 Geometric group theory
Full Text: DOI arXiv
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