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Infinite systolic groups are not torsion

Volume 153 / 2018

Tomasz Prytuła Colloquium Mathematicum 153 (2018), 169-194 MSC: 20F65, 05E45, 05E18. DOI: 10.4064/cm6982-6-2017 Published online: 30 April 2018

Abstract

We study $k$-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.

Authors

  • Tomasz PrytułaSchool of Mathematics
    University of Southampton
    Southampton SO17 1BJ, UK
    e-mail

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