Volume 11, issue 2 (2007)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Filling invariants of systolic complexes and groups

Tadeusz Januszkiewicz and Jacek Świątkowski

Geometry & Topology 11 (2007) 727–758
Abstract

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.

Keywords
systolic complex, systolic group, filling radius, word-hyperbolic group, asymptotic invariant
Mathematical Subject Classification 2000
Primary: 20F69, 20F67
Secondary: 20F65
References
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Publication
Received: 13 July 2005
Revised: 15 March 2007
Accepted: 10 October 2006
Published: 10 May 2007
Proposed: Martin Bridson
Seconded: Steve Ferry, Tobias Colding
Authors
Tadeusz Januszkiewicz
Department of Mathematics
The Ohio State University
231 W 18th Ave
Columbus, OH 43210
USA
and the Mathematical Institute of Polish Academy of Sciences
Jacek Świątkowski
Instytut Matematyczny
Uniwersytet Wrocławski
pl. Grunwaldzki 2/4
50-384 Wrocław
Poland