Geometry & Topology, Vol. 5 (2001) Paper no. 17, pages 521--550.

Metric characterizations of spherical and Euclidean buildings

Ruth Charney, Alexander Lytchak

Abstract. A building is a simplicial complex with a covering by Coxeter complexes (called apartments) satisfying certain combinatorial conditions. A building whose apartments are spherical (respectively Euclidean) Coxeter complexes has a natural piecewise spherical (respectively Euclidean) metric with nice geometric properties. We show that spherical and Euclidean buildings are completely characterized by some simple, geometric properties.

Keywords. Buildings, CAT(0) spaces, spherical buildings, Euclidean buildings, metric characterisation

AMS subject classification. Primary: 20E42. Secondary: 20F65.

DOI: 10.2140/gt.2001.5.521

E-print: arXiv:math.MG/0106188

Submitted to GT on 23 November 2000. (Revised 11 May 2001.) Paper accepted 18 May 2001. Paper published 21 May 2001.

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Ruth Charney, Alexander Lytchak

Mathematics Department, Ohio State University
231 W 18th Ave, Columbus, OH 43210, USA

Mathematisches Institut der Universitat Bonn
Wegelerstrasse 10, D-53115 Bonn, Germany

Email: charney@math.ohio-state.edu, lytchak@math.uni-bonn.de

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