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arXiv · 1909.13749

Tree amalgamations and hyperbolic boundaries

Matthias Hamann
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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.

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Matthias Hamann. 2019-09-30. Tree amalgamations and hyperbolic boundaries. https://arxiv.org/abs/1909.13749

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