Groups with arbitrary cubical dimension gap

2019/12/11 by Kropholler, Robert, O'Donnell, Chris
#20F65 #20F67 #57M07 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1912.05055

Abstract

We prove that if G = G₁×…× G_n acts essentially, properly and cocompactly on a CAT(0) cube complex X, then the cube complex splits as a product. We use this theorem to give various examples of groups for which the minimal dimension of a cube complex the group acts on is strictly larger than that of the minimal dimension of a CAT(0) space upon which the group acts.

Related

• Product separability for special cube complexes
• Coarse obstructions to cocompact cubulation
• On the Girth of Groups acting on CAT(0) cube complexes
• The Tits alternative for CAT(0) cubical complexes
• Median sets of isometries in CAT(0) cube complexes and some applications