Geometry & Topology
- Geom. Topol.
- Volume 5, Number 2 (2001), 521-550.
Metric characterizations of spherical and Euclidean buildings
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.
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
Permanent link to this document
Digital Object Identifier
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]
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. https://projecteuclid.org/euclid.gt/1513883036