Boundaries of systolic groups

Osajda, Damian¹ ; Przytycki, Piotr²

¹ Instytut Matematyczny, Uniwersytet Wrocławski, pl Grunwaldzki 2/4, 50–384 Wrocław, Poland
² Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warsaw, Poland

Geometry & topology, Tome 13 (2009) no. 5, pp. 2807-2880.

Résumé

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 $CAT\left(0\right)$ spaces.

Détail

DOI : 10.2140/gt.2009.13.2807

Keywords: systolic group, simplicial nonpositive curvature, boundaries of groups, $Z$–set compactification

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