2014/08/31 by Rudolf Zeidler · 1 citation
Mathematics · #Advanced Operator Algebra Research #Automorphism #Automorphism group #Combinatorics #Conjugacy class #Covering space #Differential geometry #Discrete mathematics #Geometric and Algebraic Topology #Geometry #Group (periodic table) #Homomorphism #Homotopy and Cohomology in Algebraic Topology #Hyperbolic geometry #Hyperbolic group #Hyperbolic manifold #Invariant (physics) #Mapping class group #Mathematical analysis #Mathematics #Metric space #Outer automorphism group #Pure mathematics #Relatively hyperbolic group #Surface (topology) #math.GR #msc:20F65
paper · pdf · doi:10.1007/s10711-015-0090-8
published as Geom. Dedicata 180 (2016), 49-68 · 23 pages, v2: Minor revision following the referee's suggestions. The final publication is available at link.springer.com via https://doi.org/10.1007/s10711-015-0090-8
arxiv created 2015/06/12 · openalex publication_date 2015/06/12 · arxiv updated 2016/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We study Bowditch's notion of a coarse median on a metric space and formally introduce the concept of a coarse median structure as an equivalence class of coarse medians up to closeness. We show that a group which possesses a uniformly left-invariant coarse median structure admits only finitely many conjugacy classes of homomorphisms from a given group with Kazhdan's property (T). This is a common generalization of a theorem due to Paulin about the outer automorphism group of a hyperbolic group with property (T) as well as of a result of Behrstock-Drutu-Sapir on the mapping class groups of orientable surfaces. We discuss a metric approximation property of finite subsets in coarse median spaces extending the classical result on approximation of Gromov hyperbolic spaces by trees.