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On Ptolemaic metric simplicial complexes

Published online by Cambridge University Press:  10 May 2010

S. M. BUCKLEY ,
D. J. WRAITH  and
J. McDOUGALL
S. M. BUCKLEY
Affiliation:
Department of Mathematics, National University of Ireland Maynooth, Maynooth, Co. Kildare, Ireland. e-mail: stephen.buckley@nuim.iedavid.wraith@nuim.ie
D. J. WRAITH
Affiliation:
Department of Mathematics, National University of Ireland Maynooth, Maynooth, Co. Kildare, Ireland. e-mail: stephen.buckley@nuim.iedavid.wraith@nuim.ie
J. McDOUGALL
Affiliation:
Department of Mathematics and Computer Science, Colorado College, Colorado Springs, Colorado 80903, U.S.A. e-mail: JMcDougall@ColoradoCollege.edu.
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Abstract

We show that under certain mild conditions, a metric simplicial complex which satisfies the Ptolemy inequality is a CAT(0) space. Ptolemy's inequality is closely related to inversions of metric spaces. For a large class of metric simplicial complexes, we characterize those which are isometric to Euclidean space in terms of metric inversions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 149 , Issue 1 , July 2010 , pp. 93 - 104
Copyright
Copyright © Cambridge Philosophical Society 2010

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References

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