The Gromov boundary of the ray graph

Juliette Bavard (1, 2) , Alden Walker

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Domaines: Topologie géométrique [math.GT]

Juliette Bavard, Alden Walker. The Gromov boundary of the ray graph. Transactions of the American Mathematical Society, 2018, 370 (11), pp.7647-7678. ⟨10.1090/tran/7204⟩. ⟨hal-01884638⟩