On finite arithmetic simplicial complexes

Papikian, Mihran

doi:10.1090/S0002-9939-2010-10605-6

On finite arithmetic simplicial complexes
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Proc. Amer. Math. Soc. 139 (2011), 111-124 Request permission

Abstract:

We compute the Euler-Poincaré characteristic of quotients of the Bruhat-Tits building of $\operatorname {PGL}(n)$ under the action of arithmetic groups arising from central division algebras over rational function fields of positive characteristic. We use this result to determine the structure of the quotient simplicial complex in certain cases.

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