Explicit Constructions of Universal R‐Trees and Asymptotic Geometry of Hyperbolic Spaces | Zendy

Dyubina Anna | Zendy; Polterovich Iosif | Zendy

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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.

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