Metric characterizations of spherical, and Euclidean buildings

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.

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

Cited by in corpus (3)

• A geometric construction of panel-regular lattices in buildings of types ~A_2 and ~C_2
• A rank rigidity result for CAT(0) spaces with one-dimensional Tits boundaries
• Spherical subcomplexes of spherical buildings