Ramanujan Complexes of Type Ad
Alex Lubotzky, Beth Samuels, Uzi Vishne
Abstract
We define and construct Ramanujan complexes. These are simplicial complexes which are higher dimensional analogues of Ramanujan graphs. They are obtained as quotients of the buildings of type Ad-1 associated with PGLd(F) where F is a local field of positive characteristic.
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