The Gromov boundary of the ray graph

Bavard, Juliette; Walker, Alden

doi:10.1090/tran/7204

The Gromov boundary of the ray graph
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by Juliette Bavard and Alden Walker PDF

Trans. Amer. Math. Soc. 370 (2018), 7647-7678 Request permission

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.

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