Random groups have fixed points on 𝐶𝐴𝑇(0) cube complexes

Fujiwara, Koji; Toyoda, Tetsu

doi:10.1090/S0002-9939-2011-11343-1

Random groups have fixed points on $\mathrm {CAT}(0)$ cube complexes
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by Koji Fujiwara and Tetsu Toyoda PDF

Proc. Amer. Math. Soc. 140 (2012), 1023-1031 Request permission

Abstract:

We prove that a random group has fixed points when it isometrically acts on a $\textrm {CAT}(0)$ cube complex. We do not assume that the action is simplicial.

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