Torsion groups do not act on $2$-dimensional $\mathrm{CAT}(0)$ complexes

Sergey Norin, Damian Osajda, Piotr Przytycki

We show, under mild hypotheses, that if each element of a finitely generated group acting on a $2$-dimensional $\mathrm{CAT}(0)$ complex has a fixed point, then there is a global f…