The Gromov boundary of the ray graph

2016/08/16 by Juliette Bavard, Bavard, Juliette, Alden Walker +1 · 1 citation
Mathematics · #20F65 #20F67 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1608.04475

openalex publication_date 2016/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• The number of ends of big mapping class groups

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