an:05876236
Zbl 1222.57013
Mj, Mahan; Pal, Abhijit
Relative hyperbolicity, trees of spaces and Cannon-Thurston maps
EN
Geom. Dedicata 151, 59-78 (2011).
00276653
2011
j
57M50 20F65
relative hyperbolicity; Cannon-Thurston maps; trees of spaces
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 \textit{M. Bestvina} and \textit{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.
Joan Porti (Bellaterra)
Zbl 0724.57029