Let be the metric product of a symmetric space of noncompact type, a Euclidean space and a product of Euclidean buildings. Let be a discrete group acting isometrically and cocompactly on . We determine a family of quasi-isometry invariants for such , namely the -dimensional Dehn functions, which measure the difficulty to fill -spheres by -balls (for ). Since the group is quasi-isometric to the associated CAT(0) space , assertions about Dehn functions for are equivalent to the corresponding results on filling functions for . Basic examples of groups as above are uniform -arithmetic subgroups of reductive groups defined over global fields. We also discuss a (mostly) conjectural picture for non-uniform -arithmetic groups.
Cite this article
Enrico Leuzinger, Optimal higher-dimensional Dehn functions for some CAT(0) lattices. Groups Geom. Dyn. 8 (2014), no. 2, pp. 441–466DOI 10.4171/GGD/233