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Transactions of the American Mathematical Society

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The Gromov boundary of the ray graph


Authors: Juliette Bavard and Alden Walker
Journal: Trans. Amer. Math. Soc. 370 (2018), 7647-7678
MSC (2010): Primary 20F65, 37E30, 57M60, 05C63
DOI: https://doi.org/10.1090/tran/7204
Published electronically: April 17, 2018
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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.


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Additional Information

Juliette Bavard
Affiliation: Institut de Mathématiques de Jussieu-Paris Rive Gauche, UPMC
Address at time of publication: Univ Rennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes, France
Email: juliette.bavard@univ-rennes1.fr

Alden Walker
Affiliation: Center for Communications Research, La Jolla, California 92121
Email: akwalke@ccrwest.org

DOI: https://doi.org/10.1090/tran/7204
Received by editor(s): November 2, 2016
Received by editor(s) in revised form: January 19, 2017
Published electronically: April 17, 2018
Article copyright: © Copyright 2018 American Mathematical Society

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