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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Wienhard, Anna

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1435-5337
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Volume 19, Issue 6 (Nov 2007)

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On the simple connectedness of certain subsets of buildings

Alice Devillers
  • Université Libre de Bruxelles, Département de Mathématiques—C.P.216, Boulevard du Triomphe, B-1050 Brussels, Belgium.
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/ Bernhard Mühlherr
  • Université Libre de Bruxelles, Département de Mathématiques—C.P.216, Boulevard du Triomphe, B-1050 Brussels, Belgium.
  • Email:
Published Online: 2007-11-19 | DOI: https://doi.org/10.1515/FORUM.2007.037

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].

About the article


Received: 2005-09-12

Revised: 2005-11-17

Accepted: 2005-11-21

Published Online: 2007-11-19

Published in Print: 2007-11-20


Citation Information: Forum Mathematicum, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/FORUM.2007.037.

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Citing Articles

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[1]
Rieuwert J. Blok and Corneliu Hoffman
Journal of Algebra, 2008, Volume 319, Number 11, Page 4662
[2]
Rieuwert J. Blok and Corneliu G. Hoffman
Journal of Algebra, 2014, Volume 399, Page 978
[3]
Rieuwert J. Blok and Corneliu Hoffman
Journal of Algebra, 2009, Volume 321, Number 4, Page 1196
[4]
Alice Devillers, Bernhard Mühlherr, and Hendrik Van Maldeghem
Mathematische Annalen, 2012, Volume 354, Number 1, Page 297
[5]
Ralf Gramlich, Max Horn, and Bernhard Mühlherr
Journal of Group Theory, 2011, Volume 14, Number 2

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