Abstract
We define and construct Ramanujan complexes. These are simplicial complexes which are higher dimensional analogues of Ramanujan graphs (constructed in [LPS]). They are obtained as quotients of the buildings of typeà d−1 associated with PGL d (F) whereF is a local field of positive characteristic.
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With love and admiration to Hillel Furstenberg, a teacher and friend
The authors were partially supported by grants from NSF and BSF (U.S.-Israel).
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Lubotzky, A., Samuels, B. & Vishne, U. Ramanujan complexes of typeà d . Isr. J. Math. 149, 267–299 (2005). https://doi.org/10.1007/BF02772543
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DOI: https://doi.org/10.1007/BF02772543