Volume 11, issue 2 (2007)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 6, 2483–2999
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
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
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
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