New York Journal of Mathematics
Volume 19 (2013) 13-22


Stephen M. Buckley and Kurt Falk

Natural maps between CAT(0) boundaries

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Published: February 4, 2013
Keywords: CAT(0) space, Gromov hyperbolic space, ideal boundary, Gromov boundary, natural map
Subject: Primary 51M05, 51M10. Secondary: 51F99

It is shown that certain natural maps between the ideal, Gromov, and end boundaries of a complete CAT(0) space can fail to be either injective or surjective. Additionally the natural map from the Gromov boundary to the end boundary of a complete CAT(-1) space can fail to be either injective or surjective.


Both authors thank the University of Bremen and National University of Ireland Maynooth for hospitality and financial support of reciprocal visits that enabled this research effort.

Author information

Stephen M. Buckley:
Department of Mathematics and Statistics, National University of Ireland Maynooth, Maynooth, Co. Kildare, Ireland

Kurt Falk:
Universität Bremen, FB 3 - Mathematik, Bibliothekstra{\ss}e 1, 28359 Bremen, Germany