# Infinite systolic groups are not torsion

@article{Prytula2018InfiniteSG, title={Infinite systolic groups are not torsion}, author={Tomasz Prytula}, journal={Colloquium Mathematicum}, year={2018}, volume={153}, pages={169-194} }

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… CONTINUE READING

8 Citations

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 12 REFERENCES