Tree amalgamations and hyperbolic boundaries
Combinatorics
2019-10-01 v1
Abstract
We look at tree amalgamations of locally finite quasi-transitive hyperbolic graphs and prove that the homeomorphism type of the hyperbolic boundary of such a tree amalgamation only depends on the homeomorphism types of the hyperbolic boundaries of their factors. Additionally, we show that two locally finite quasi-transitive hyperbolic graphs have homeomorphic hyperbolic boundaries if and only if the homeomorphism types of the hyperbolic boundaries of the factors of their terminal factorisations coincide.
Cite
@article{arxiv.1909.13749,
title = {Tree amalgamations and hyperbolic boundaries},
author = {Matthias Hamann},
journal= {arXiv preprint arXiv:1909.13749},
year = {2019}
}
Comments
9 pages