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Paul R. Brown
Buildings and Non-positively Curved Polygons of Finite Groups
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| Published: |
November 11, 1998 |
| Keywords: |
triangle of groups, polygon of groups, nonpositive curvature, Euclidean building, hyperbolic building, periodic flats |
| Subject: |
20F32, 51E24 |
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Abstract
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.
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| Acknowledgements
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.
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| 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
prb@uic.edu
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