We prove that the boundary of a right-angled hyperbolic building is a universal Menger space. As a consequence, the 3-dimensional universal Menger space is the boundary of some Gromov-hyperbolic group.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm197-0-6,
author = {Jan Dymara and Damian Osajda},
title = {Boundaries of right-angled hyperbolic buildings},
journal = {Fundamenta Mathematicae},
volume = {193},
year = {2007},
pages = {123-165},
zbl = {1177.20042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm197-0-6}
}
Jan Dymara; Damian Osajda. Boundaries of right-angled hyperbolic buildings. Fundamenta Mathematicae, Tome 193 (2007) pp. 123-165. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm197-0-6/