JournalsggdVol. 8, No. 2pp. 441–466

Optimal higher-dimensional Dehn functions for some CAT(0) lattices

  • Enrico Leuzinger

    Karlsruhe Institute of Technology (KIT), Germany
Optimal higher-dimensional Dehn functions for some  CAT(0) lattices cover
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Abstract

Let X=S×E×BX=S\times E \times B be the metric product of a symmetric space SS of noncompact type, a Euclidean space EE and a product BB of Euclidean buildings. Let Γ\Gamma be a discrete group acting isometrically and cocompactly on XX. We determine a family of quasi-isometry invariants for such Γ\Gamma, namely the kk-dimensional Dehn functions, which measure the difficulty to fill kk-spheres by (k+1)(k+1)-balls (for 1kdim X11\leq k\leq \dim\ X-1). Since the group Γ\Gamma is quasi-isometric to the associated CAT(0) space XX, assertions about Dehn functions for Γ\Gamma are equivalent to the corresponding results on filling functions for XX. Basic examples of groups Γ\Gamma as above are uniform SS-arithmetic subgroups of reductive groups defined over global fields. We also discuss a (mostly) conjectural picture for non-uniform SS-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. 441–466

DOI 10.4171/GGD/233