New York Journal of Mathematics
Volume 4 (1998) 237-248


Paul R. Brown

Buildings and Non-positively Curved Polygons of Finite Groups

Published: November 11, 1998
Keywords: triangle of groups, polygon of groups, nonpositive curvature, Euclidean building, hyperbolic building, periodic flats
Subject: 20F32, 51E24

Let P be a non-positively curved polygon of finite groups. The group P acts on a contractible 2-complex XP, and we prove that this complex is a building if and only if the links have (angular) diameter \pi. When P has zero group theoretic curvature, a geometric argument shows that the periodic apartments are dense in the set of all apartments.


This work is based on research partly supported by the National Science Foundation under Grant No. DMS-9503034 and initially appeared as a chapter in the author's dissertation.

Author information

Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720, USA
Current Address: Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL 60607