Volume 13, issue 5 (2009)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Boundaries of systolic groups

Damian Osajda and Piotr Przytycki

Geometry & Topology 13 (2009) 2807–2880
Abstract

For all systolic groups we construct boundaries which are EZ–structures. This implies the Novikov conjecture for torsion-free systolic groups. The boundary is constructed via a system of distinguished geodesics in a systolic complex, which we prove to have coarsely similar properties to geodesics in CAT(0) spaces.

Keywords
systolic group, simplicial nonpositive curvature, boundaries of groups, $Z$–set compactification
Mathematical Subject Classification 2000
Primary: 20F65, 20F67
Secondary: 20F69
References
Publication
Received: 18 August 2008
Revised: 15 July 2009
Accepted: 8 May 2009
Published: 17 August 2009
Proposed: Wolfgang Lück
Seconded: Jean-Pierre Otal, Martin Bridson
Authors
Damian Osajda
Instytut Matematyczny
Uniwersytet Wrocławski
pl Grunwaldzki 2/4
50–384 Wrocław
Poland
Piotr Przytycki
Institute of Mathematics
Polish Academy of Sciences
Śniadeckich 8
00-956 Warsaw
Poland