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Two-dimensional finite non-positively curved polyhedra of rank two. (Polyèdres finis de dimension 2 à courbure \(\leq 0\) et de rang 2.) (French) Zbl 0831.53031
Summary: We locally define the notion of polyhedra of rank two for two-dimensional finite non-positively curved polyhedra. We prove that the universal covering of such a space is either the product of two trees or an Euclidean Tits building of rank two.

MSC:
53C35 Differential geometry of symmetric spaces
51E24 Buildings and the geometry of diagrams
51M20 Polyhedra and polytopes; regular figures, division of spaces
20E42 Groups with a \(BN\)-pair; buildings
05C12 Distance in graphs
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References:
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[2] K.S. BROWN, Buildings, Springer-Verlag, New York, 1989. · Zbl 0715.20017
[3] K.S. BROWN, Five lectures on buildings, Congrès de Trieste 1990. · Zbl 0846.20032
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[8] M. BRIDSON, A. HAEFLIGER, Livre en préparation.
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