Cubulating spaces with walls. (English) Zbl 1131.20030

From the introduction: The elegant notion of a space with walls was introduced by F. Haglund and F. Paulin [Geom. Topol. Monogr. 1, 181-248 (1998; Zbl 0916.51019)]. Prototypical examples of spaces with walls are CAT(0) cube complexes, introduced by M. Gromov [in Essays in group theory, Publ., Math. Sci. Res. Inst. 8, 75-263 (1987; Zbl 0634.20015)]. The purpose of this note is to observe that every space with walls has a canonical embedding in a CAT(0) cube complex and, consequently, a group action on a space with walls extends naturally to a group action on a CAT(0) cube complex. The usefulness of this result is that spaces with walls are often easily identifiable by geometric reasons.


20F65 Geometric group theory
53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
20E42 Groups with a \(BN\)-pair; buildings
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