Random Group Actions on CAT(0) Square Complexes

2022/10/12 by Munro, Zachary
#20E08 (Secondary) #20F65 (Primary) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2210.06378

Abstract

We generalize ideas of Jahncke from trees to square complexes. We introduce the notion of progression in CAT(0) square complexes. Using progression, we are able to build on the proof strategy of Dahmani-Guirardel-Przytycki to show any action of a random group with seven or more generators on a CAT(0) square complex has a global fixed point.

Related

• Random groups have fixed points on CAT(0) cube complexes
• Random groups at density d<3/14 act non-trivially on a CAT(0) cube complex
• N-step energy of maps and fixed-point property of random groups
• Random groups are not n-cubulated
• Torsion groups do not act on 2-dimensional CAT(0) complexes