### References & Citations

# Mathematics > Geometric Topology

# Title:The Gromov boundary of the ray graph

(Submitted on 16 Aug 2016 (v1), last revised 28 Aug 2018 (this version, v2))

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.

## Submission history

From: Alden Walker [view email]**[v1]**Tue, 16 Aug 2016 04:12:02 UTC (1,081 KB)

**[v2]**Tue, 28 Aug 2018 03:43:28 UTC (1,080 KB)