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EXPLICIT CONSTRUCTIONS OF UNIVERSAL ℝ-TREES AND ASYMPTOTIC GEOMETRY OF HYPERBOLIC SPACES

Published online by Cambridge University Press:  28 November 2001

ANNA DYUBINA  and
IOSIF POLTEROVICH
ANNA DYUBINA
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Israel; annadi@math.tau.ac.il
IOSIF POLTEROVICH
Affiliation:
Department of Mathematics, The Weizmann Institute of Science, Rehovot, Israel; iossif@wisdom.weizmann.ac.il
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Abstract

This paper presents explicit constructions of universal ℝ-trees as certain spaces of functions, and also proves that a 2ℵ0-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.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 6 , November 2001 , pp. 727 - 734
Copyright
© The London Mathematical Society 2001

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