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Filling invariants of systolic complexes and groups. (English) Zbl 1188.20043
Summary: Systolic complexes are simplicial analogues of nonpositively curved spaces. Their theory seems to be largely parallel to that of CAT(0) cubical complexes.
We study the filling radius of spherical cycles in systolic complexes, and obtain several corollaries. We show that a systolic group can not contain the fundamental group of a nonpositively curved Riemannian manifold of dimension strictly greater than 2, although there exist word hyperbolic systolic groups of arbitrary cohomological dimension.
We show that if a systolic group splits as a direct product, then both factors are virtually free. We also show that systolic groups satisfy linear isoperimetric inequality in dimension 2.

MSC:
20F67 Hyperbolic groups and nonpositively curved groups
20F69 Asymptotic properties of groups
20F65 Geometric group theory
57M07 Topological methods in group theory
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