Infinite systolic groups are not torsion

Prytuła, Tomasz (2018) Infinite systolic groups are not torsion. Colloquium Mathematicum, 153 (2), 169-194. (doi:10.4064/cm6982-6-2017).

Abstract

We study k-systolic complexes introduced by T. Januszkiewicz and J. Swiatkowski, which are simply connected simplicial complexes of simplicial nonpositive curvature. Using techniques of filling diagrams we prove that for k ≥ 7 the 1-skeleton of a k-systolic complex is Gromov hyperbolic. We give an elementary proof of the so-called Projection Lemma, which implies contractibility of 6-systolic complexes. We also present a new proof of the fact that an infinite group acting geometrically on a 6-systolic complex is not torsion.

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