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

2010/12/19 by Fujiwara, Koji, Toyoda, Tetsu
#20P05 #51F99 #FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG) #Primary 53C23 #Secondary 20F65

paper · doi:10.48550/arxiv.1012.4147

Abstract

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

Related

• Random Group Actions on CAT(0) Square Complexes
• A condition that prevents groups from acting fixed point free on cube complexes
• Random groups at density d<3/14 act non-trivially on a CAT(0) cube complex
• Random groups are not n-cubulated
• Isometries of CAT(0) cube complexes are semi-simple