Geodesic
Optimal higher-dimensional Dehn functions for some CAT(0) lattices
Enrico Leuzinger1
1Karlsruhe Institute of Technology (KIT), Germany
Groups, geometry, and dynamics, Tome 8 (2014) no. 2, pp. 441-466

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DOI

Let X=S×E×B be the metric product of a symmetric space S of noncompact type, a Euclidean space E and a product B of Euclidean buildings. Let Γ be a discrete group acting isometrically and cocompactly on X. We determine a family of quasi-isometry invariants for such Γ, namely the k-dimensional Dehn functions, which measure the difficulty to fill k-spheres by (k+1)-balls (for 1≤k≤dim X−1). Since the group Γ is quasi-isometric to the associated CAT(0) space X, assertions about Dehn functions for Γ are equivalent to the corresponding results on filling functions for X. Basic examples of groups Γ as above are uniform S-arithmetic subgroups of reductive groups defined over global fields. We also discuss a (mostly) conjectural picture for non-uniform S-arithmetic groups.
DOI : 10.4171/ggd/233
Classification : 00-XX
Mots-clés : Filling functions, higher-dimensional Dehn functions, isoperimetric inequalities, symmetric spaces, Euclidean buildings, lattices, S-arithmetic groups

Enrico Leuzinger  1

1 Karlsruhe Institute of Technology (KIT), Germany 
Enrico Leuzinger. Optimal higher-dimensional Dehn functions for some  CAT(0) lattices. Groups, geometry, and dynamics, Tome 8 (2014) no. 2, pp. 441-466. doi: 10.4171/ggd/233
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     title = {Optimal higher-dimensional {Dehn} functions for some  {CAT(0)} lattices},
     journal = {Groups, geometry, and dynamics},
     pages = {441--466},
     year = {2014},
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     number = {2},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/233/}
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