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Journal of the London Mathematical Society Advance Access originally published online on September 30, 2009
Journal of the London Mathematical Society 2009 80(3):649-664; doi:10.1112/jlms/jdp047
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© 2009 London Mathematical Society

Fundamental pro-groups and Gromov boundaries of 7-systolic groups

Jacek Swiatkowski

Instytut Matematyczny
Uniwersytet Wroclawski
pl. Grunwaldzki 2/4
50-384 Wroclaw
Poland

We introduce the property of pro-{pi}1-saturation (defined in terms of fundamental pro-groups) for compact metric spaces. We expect (though cannot yet prove) this property to be stronger than hereditary asphericity. We show that 1-dimensional spaces and Gromov boundaries of 7-systolic groups are pro-{pi}1-saturated (the latter class contains examples of pro-{pi}1-saturated spaces with arbitrary finite topological dimension).

2000 Mathematics Subject Classification 20F67, 20F65, 55P55, 55Q07.

Partially supported by Polish Ministry of Research and Higher Education (MNiSW) grant N201 012 32/0718.

Received July 10, 2008; revised April 9, 2009; published online September 30, 2009.


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