2017/11/29 by Davide Spriano, Spriano, Davide
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR
paper · pdf · doi:10.48550/arxiv.1711.10931
36 pages, 3 figures, streamlined and clarified some arguments, corrected typos. arXiv admin note: text overlap with arXiv:1604.01061 by other authors
arxiv created 2018/12/12 · arxiv updated 2018/12/17
In this paper we provide a procedure to obtain a non-trivial HHS structure on a hyperbolic space. In particular, we prove that given a finite collection F of quasi-convex subgroups of a hyperbolic group G, there is an HHG structure on G that is compatible with F. We will use this to provide explicit descriptions of the Gromov Boundary of hyperbolic HHS and HHG, and we recover results from Hamenstädt, Manning, Trang for the case when G is hyperbolic relative to F. Further applications in the construction of new HHG will be presented in a subsequent paper.