Filling invariants of systolic complexes and groups

Systolic complexes were introduced in Januszkiewicz–Świa̧tkowski [12] and, independently, in Haglund [10]. They are simply connected simplicial complexes satisfying a certain condition that we call simplicial nonpositive curvature (abbreviated SNPC). The condition is local and purely combinatorial. It neither implies nor is implied by nonpositive curvature for geodesic metrics on complexes, but it has many similar consequences. It is a simplicial analogue of the combinatorial condition for cubical complexes equivalent to nonpositive curvature for the standard piecewise Euclidean cubical metric, namely the flag property for links at vertices.