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Abstract
We prove a rank 3 criterion for the simple connectedness of certain subsets of buildings and we give two applications of this criterion. The first generalizes a result of Tits for Chevalley groups to 3-spherical Kac-Moody groups. The second is the proof of the simple connectedness of certain flipflop geometries introduced in [Bennett C., Gramlich R., Hoffman C., Shpectorov S.: Curtis-Phan-Tits theory. In: Groups, combinatorics and geometry (Durham, 2001). World Sci. Publishing, River Edge, NJ, 2003, 13–29].
Received: 2005-09-12
Revised: 2005-11-17
Accepted: 2005-11-21
Published Online: 2007-11-19
Published in Print: 2007-11-20
© Walter de Gruyter
