Geometry & Topology

Metric characterizations of spherical and Euclidean buildings

Ruth Charney and Alexander Lytchak

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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.

Article information

Geom. Topol., Volume 5, Number 2 (2001), 521-550.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20E42: Groups with a $BN$-pair; buildings [See also 51E24]
Secondary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

buildings CAT(0) spaces spherical buildings Euclidean buildings metric characterisation


Charney, Ruth; Lytchak, Alexander. Metric characterizations of spherical and Euclidean buildings. Geom. Topol. 5 (2001), no. 2, 521--550. doi:10.2140/gt.2001.5.521.

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