On Ptolemaic metric simplicial complexes
Buckley, S.M. and Wraith, D.J. and McDougall, J. (2010) On Ptolemaic metric simplicial complexes. Mathematical Proceedings of the Cambridge Philosophical Society, 149 (1). pp. 93-104. ISSN 1469-8064
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.
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