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Noncommutative geometry on trees and buildings

Cornelissen, Gunther and Marcolli, Matilde and Reihani, Kamran and Vdovina, Alina (2006) Noncommutative geometry on trees and buildings. . (Submitted)

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We describe the construction of theta summable and finitely summable spectral triples associated to Mumford curves and some classes of higher dimensional buildings. The finitely summable case is constructed by considering the stabilization of the algebra of the dual graph of the special fiber of the Mumford curve and a variant of the Antonescu-Christensen spectral geometries for AF algebras. The information on the Schottky uniformization is encoded in the spectral geometry through the Patterson-Sullivan measure on the limit set. Some higher rank cases are obtained by adapting the construction for trees.

Item Type:Report or Paper (Discussion Paper)
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Record Number:CaltechAUTHORS:20170713-083009140
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79063
Deposited By: Tony Diaz
Deposited On:13 Jul 2017 16:23
Last Modified:03 Oct 2019 18:15

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