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Explicit Constructions of Universal R‐Trees and Asymptotic Geometry of Hyperbolic Spaces
Author(s) -
Dyubina Anna,
Polterovich Iosif
Publication year - 2001
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460930100844x
Subject(s) - mathematics , infinity , covering space , abelian group , pure mathematics , manifold (fluid mechanics) , cone (formal languages) , mathematical analysis , mechanical engineering , engineering , algorithm
This paper presents explicit constructions of universal R‐trees as certain spaces of functions, and also proves that a2 ℵ 0‐universal R‐tree can be isometrically embedded at infinity into a complete simply connected manifold of negative curvature, or into a non‐abelian free group. In contrast to asymptotic cone constructions, asymptotic spaces are built without using the axiom of choice. 2000 Mathematics Subject Classification L53C23, 20F67.