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Filling invariants of
systolic complexes and groups
Tadeusz Januszkiewicz and Jacek Świątkowski |
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Geometry & Topology 11 (2007) 727–758
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Abstract |
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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. |
Keywords
systolic complex, systolic group, filling radius,
word-hyperbolic group, asymptotic invariant
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Mathematical Subject Classification 2000
Primary: 20F69, 20F67
Secondary: 20F65
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References |
Forward citations |
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
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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 |
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| Jacek Świątkowski | |
| Instytut Matematyczny Uniwersytet Wrocławski pl. Grunwaldzki 2/4 50-384 Wrocław Poland |
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