The Gromov boundary of the ray graph

Juliette Bavard; Alden Walker

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arXiv · 1608.04475

The Gromov boundary of the ray graph

Juliette Bavard·Alden Walker

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Abstract

The ray graph is a Gromov hyperbolic graph on which the mapping class group of the plane minus a Cantor set acts by isometries. We give a description of the Gromov boundary of the ray graph in terms of cliques of long rays on the plane minus a Cantor set. As a consequence, we prove that the Gromov boundary of the ray graph is homeomorphic to a quotient of a subset of the circle. This version contains some updates and corrections.

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Juliette Bavard, Alden Walker. 2016-08-16. The Gromov boundary of the ray graph. https://arxiv.org/abs/1608.04475

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