Geometry & Topology

Filling invariants of systolic complexes and groups

Tadeusz Januszkiewicz and Jacek Świątkowski

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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.

Article information

Geom. Topol., Volume 11, Number 2 (2007), 727-758.

Received: 13 July 2005
Revised: 15 March 2007
Accepted: 10 October 2006
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F69: Asymptotic properties of groups 20F67: Hyperbolic groups and nonpositively curved groups
Secondary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

systolic complex systolic group filling radius word-hyperbolic group asymptotic invariant


Januszkiewicz, Tadeusz; Świątkowski, Jacek. Filling invariants of systolic complexes and groups. Geom. Topol. 11 (2007), no. 2, 727--758. doi:10.2140/gt.2007.11.727.

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