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

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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.

Item Type: Article
Keywords: Ptolemaic metric simplicial complexes;
Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 2420
Depositing User: Prof. Stephen Buckley
Date Deposited: 09 Feb 2011 11:13
Journal or Publication Title: Mathematical Proceedings of the Cambridge Philosophical Society
Publisher: Cambridge University Press
Refereed: Yes

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