Metric characterizations of spherical, and Euclidean buildings

Details Metric characterizations of spherical, and Euclidean buildings Metric characterizations of spherical, and Euclidean buildings

2001-06-22

arxiv.org/abs/math/0106188v1

Geom. Topol. 5(2001) 521-550

Mathematics

Metric Geometry

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper17.abs.html

Scientific paper

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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