Some properties of median metric spaces

DOI10.4171/GGD/350zbMath1376.20044OpenAlexW2327947115MaRDI QIDQ260117

Brian H. Bowditch

Publication date: 18 March 2016

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/ggd/350

zbMATH Keywords

CAT(0)cube complexmedian algebramedian metric space

Mathematics Subject Classification ID

Geometric group theory (20F65) Topological methods in group theory (57M07) Asymptotic properties of groups (20F69) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items (14)

Morse quasiflats. I ⋮ Flats in spaces with convex geodesic bicombings ⋮ Coarse median algebras: the intrinsic geometry of coarse median spaces and their intervals ⋮ Coarse median structures and homomorphisms from Kazhdan groups ⋮ Large-scale rigidity properties of the mapping class groups ⋮ Roller boundaries for median spaces and algebras ⋮ Coarse-median preserving automorphisms ⋮ Homotopy equivalent boundaries of cube complexes ⋮ Median pretrees and functions of bounded variation ⋮ Median and injective metric spaces ⋮ Large-scale rank and rigidity of the Teichmüller metric ⋮ Superrigidity of actions on finite rank median spaces ⋮ The Tits alternative for finite rank median spaces ⋮ Large-scale rank and rigidity of the Weil-Petersson metric

Cites Work

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• Gromov's theorem on groups of polynomial growth and elementary logic
• Kazhdan and Haagerup properties from the median viewpoint.
• Higher connectedness of asymptotic cones.
• Large-scale rigidity properties of the mapping class groups
• Median algebras
• Coarse median spaces and groups.
• Graphs of some CAT(0) complexes
• Embedding median algebras in products of trees.
• Median structures on asymptotic cones and homomorphisms into mapping class groups
• Centroids and the rapid decay property in mapping class groups
• Large-scale rank and rigidity of the Teichmüller metric
• Medians and Betweenness
• Mapping class groups are automatic

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