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Median and injective metric spaces

Published online by Cambridge University Press:  27 July 2018

BRIAN H. BOWDITCH
BRIAN H. BOWDITCH*
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CV4 7AL, Great Britain e-mail: B.H.Bowditch@warwick.ac.uk
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Abstract

We describe a construction which associates to any median metric space a pseudometric satisfying the binary intersection property for closed balls. Under certain conditions, this implies that the resulting space is, in fact, an injective metric space, bilipschitz equivalent to the original metric. In the course of doing this, we derive a few other facts about median metrics, and the geometry of CAT(0) cube complexes. One motivation for the study of such metrics is that they arise as asymptotic cones of certain naturally occurring spaces.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 1 , January 2020 , pp. 43 - 55
Copyright
Copyright © Cambridge Philosophical Society 2018 

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References

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