Geometry & Topology

Filling invariants of systolic complexes and groups

Tadeusz Januszkiewicz and Jacek Świątkowski

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799860

Digital Object Identifier
doi:10.2140/gt.2007.11.727

Mathematical Reviews number (MathSciNet)
MR2302501

Zentralblatt MATH identifier
1188.20043

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

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

Citation

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. https://projecteuclid.org/euclid.gt/1513799860


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