The Ramanujan Property for Regular Cubical Complexes

  title={The Ramanujan Property for Regular Cubical Complexes},
  author={Bruce W M Jordan and RON LIVN{\'E}},
We consider cubical complexes which are uniformized by an ordered product of regular trees. For these we define the notion of being Ramanujan, generalizing the one-dimensional definition introduced by Lubotzky, Phillips, and Sarnak [15]. As in [12], we also allow local systems. We discuss the significance of this property, and then we construct explicit arithmetic examples using quaternion algebras over totally real fields. Here we reduce the Ramanujan property to special cases of the Ramanujan… CONTINUE READING

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