The extremal symmetry of arithmetic simplicial complexes

2010/06/18 by Benson Farb, Amir Mohammadi, Farb, Benson +1
Mathematics · #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR) #math.AT #math.DG #math.GR

paper · pdf · doi:10.48550/arxiv.1006.3730

17 pages

arxiv created 2010/06/18 · arxiv updated 2010/06/21

Abstract

Let G be a higher-rank semisimple Lie group over a nonarchimedean local field, for example G=\rm PGL(n,Q_P). To any lattice L in G there is an associated simplicial complex B_L, given by the quotient by L of the Bruhat-Tits building associated to G. In this paper prove that the simplicial structure B_L exhibits some remarkable and extremal symmetry properties, in particular when compared to any other simplicial structure on (any cover of) B_L.

Related

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