A Metric Characterization of Spherical Buildings
by
Ruth Charney
Ohio State University

Let X be a spherical building. It was shown by Davis that the natural piecewise spherical metric on X, in which each apartment is isometric to a standard sphere, is a CAT(1) space. In addition, since any two points are contained in an apartment, X has diameter \pi, as does the link of any simplex in X. We prove that these metric conditions characterize (thick) spherical buildings. More precisely, if X is a CAT(1), piecewise spherical cell complex satisfying

1. X is connected and has diameter \pi,

2. for k < n-1, Link(\sigma^k, X) is connected and has diameter \pi,

3. Link(\sigma^n-1, X) contains at least 3 points,

Date received: March 10, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caca-66.