Trees, ultrametrics, and noncommutative geometry

DOI10.4310/PAMQ.2012.v8.n1.a11zbMath1251.46038arXivmath/0605131MaRDI QIDQ429571

Bruce Hughes

Publication date: 20 June 2012

Published in: Pure and Applied Mathematics Quarterly (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605131

zbMATH Keywords

ultrametric spaceBratteli diagramlocal isometrylocal similaritynon-commutative ultrametric geometrysymmetry of infinity group

Mathematics Subject Classification ID

Trees (05C05) Geometric group theory (20F65) Metric spaces, metrizability (54E35) Noncommutative topology (46L85) (K_0) as an ordered group, traces (19K14)

Related Items (24)

Minimum spanning paths and Hausdorff distance in finite ultrametric spaces ⋮ Asymptotic negative type properties of finite ultrametric spaces ⋮ ROUNDNESS PROPERTIES OF ULTRAMETRIC SPACES ⋮ On the tree-likeness of hyperbolic spaces ⋮ How rigid the finite ultrametric spaces can be? ⋮ Graph inverse semigroups: their characterization and completion. ⋮ Uniqueness of best proximity pairs and rigidity of semimetric spaces ⋮ Bipartite graphs and best proximity pairs ⋮ Metric trees of generalized roundness one ⋮ Unnamed Item ⋮ On ultrametric-preserving functions ⋮ NON-COMMUTATIVE STONE DUALITY: INVERSE SEMIGROUPS, TOPOLOGICAL GROUPOIDS AND C*-ALGEBRAS ⋮ Monoid generalizations of the Richard Thompson groups. ⋮ Combinatorial properties of ultrametrics and generalized ultrametrics ⋮ On Urysohn's \(\mathbb{R}\)-tree ⋮ Inverse sequences, rooted trees and their end spaces ⋮ Compactable semilattices ⋮ Finite ultrametric balls ⋮ Galois groups and Cantor actions ⋮ The range of ultrametrics, compactness, and separability ⋮ Local similarities and the Haagerup property. With an appendix by Daniel S. Farley. ⋮ Ultrametric preserving functions and weak similarities of ultrametric spaces ⋮ On quasisymmetric mappings between ultrametric spaces ⋮ Properties and morphisms of finite ultrametric spaces and their representing trees

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