Boundaries of systolic groups

Osajda, Damian; Przytycki, Piotr

doi:10.2140/gt.2009.13.2807

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Boundaries of systolic groups

Damian Osajda and Piotr Przytycki

Geometry & Topology 13 (2009) 2807–2880

DOI: 10.2140/gt.2009.13.2807

Abstract

For all systolic groups we construct boundaries which are $E Z$ –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

Volume 13, issue 5 (2009)