GH-convergence of CAT(0)-spaces: stability of the Euclidean factor

2023/09/26 by Cavallucci, Nicola
#Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2309.14762

Abstract

We prove that if a sequence of geodesically complete CAT(0)-spaces X_j with uniformly cocompact discrete groups of isometries converges in the Gromov-Hausdorff sense to X_∞, then the dimension of the maximal Euclidean factor splitted off by X_∞ and X_j is the same, for j big enough. In other words, no additional Euclidean factors can appear in the limit.

Related

• A GH-compactification of CAT(0)-groups via totally disconnected, unimodular actions
• Convergence and collapsing of CAT(0)-lattices
• Cocompact CAT(0) spaces are almost geodesically complete
• On the boundaries of geodesically complete CAT(0) spaces
• Finiteness of CAT(0) group actions