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G^3 = Geometric Group Theory on the Gulf Coast
January 9-12, 2007

New Orleans, LA, USA

Organizers
Stephen Brick, Craig Jensen, Igor Mineyev.

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Connectivity of Spheres and Horospheres in Euclidean Buildings
by
Kai-Uwe Bux
University of Virginia
Coauthors: Kevin Wortman

Recall that a CW complex of dimension m is called spherical if it is (m-1)-connected. Let X be a Euclidean building. The Solomon-Tits theorem states that spherical buildings are spherical. Small metric spheres in X are generically (metrically distorted) spherical buildings, and therefore spherical. We generalize this result to spheres of arbitrary radius. We also consider horospheres in irreducible affine buildings.

Date received: December 12, 2006

Copyright © 2006 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 # catr-08.