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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board Member: Bannai, Eiichi / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Pasini, Antonio / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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1615-7168
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Volume 13, Issue 3 (Jul 2013)

Issues

A local-to-global result for topological spherical buildings

Rupert McCallum
Published Online: 2013-07-11 | DOI: https://doi.org/10.1515/advgeom-2012-0029

Abstract

Suppose that Δ;Δʹ are two buildings each arising from a semisimple algebraic group over a field, a topological field in the former case, and that for both the buildings the Coxeter diagram has no isolated nodes. We give conditions under which a partially defined injective chamber map, whose domain is the subcomplex of Δ generated by a nonempty open set of chambers, and whose codomain is Δʹ, is guaranteed to extend to a unique injective chamber map. Related to this result is a local version of the Borel-Tits theorem on abstract homomorphisms of simple algebraic groups.

Keywords: Topological geometry; local homomorphism; topological building; Borel-Tits theorem

About the article

Published Online: 2013-07-11

Published in Print: 2013-07-01


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2012-0029.

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