Convex cores for actions on finite-rank median algebras

2021/01/08 by Elia Fioravanti, Fioravanti, Elia · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2101.03060

openalex publication_date 2021/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that every action of a finitely generated group on a finite-rank median algebra admits a nonempty "convex core", even when no metric or topology is given. We then use this to deduce an analogue of the flat torus theorem for actions on connected finite-rank median spaces. We also prove that isometries of connected finite-rank median spaces are either elliptic or loxodromic.

Cited by

• Cocycle superrigidity for median spaces of finite rank

Related

• Isometric actions on locally compact finite rank median spaces
• Compact Median Algebras are μ-Boundaries in a unique way
• Balanced Measures on Compact Median Algebras
• Median sets of isometries in CAT(0) cube complexes and some applications
• Median geometry for spaces with measured walls and for groups