Convergence and collapsing of CAT(0)-lattices

2024/04/30 by Nicola Cavallucci, Cavallucci, Nicola, Andrea Sambusetti +1 · 1 citation
Computer Science · #Advanced Algebra and Logic #Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2405.01595

openalex publication_date 2024/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the theory of convergence for CAT(0)-lattices (that is groups Γ acting geometrically on proper, geodesically complete CAT(0)-spaces) and their quotients (CAT(0)-orbispaces). We describe some splitting and collapsing phenomena, explaining precisely how these action can degenerate to a possibly non-discrete limit action. Finally, we prove a compactness theorem for the class of compact CAT(0)-homology orbifolds, and some applications: an isolation result for flat orbispaces and an entropy-pinching theorem.

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