Infinite systolic groups are not torsion
Tom 153 / 2018
Streszczenie
We study -systolic complexes introduced by T. Januszkiewicz and J. Świątkowski, which are simply connected simplicial complexes of simplicial nonpositive curvature. Using techniques of filling diagrams we prove that for k \geq 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.