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2001 Metric characterizations of spherical and Euclidean buildings
Ruth Charney, Alexander Lytchak
Geom. Topol. 5(2): 521-550 (2001). DOI: 10.2140/gt.2001.5.521

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.

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Ruth Charney. Alexander Lytchak. "Metric characterizations of spherical and Euclidean buildings." Geom. Topol. 5 (2) 521 - 550, 2001. https://doi.org/10.2140/gt.2001.5.521

Information

Received: 23 November 2000; Revised: 11 May 2001; Accepted: 18 May 2001; Published: 2001
First available in Project Euclid: 21 December 2017

zbMATH: 1002.51008
MathSciNet: MR1833752
Digital Object Identifier: 10.2140/gt.2001.5.521

Subjects:
Primary: 20E42
Secondary: 20F65

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

Rights: Copyright © 2001 Mathematical Sciences Publishers

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