Abstract
We study bimodule quantum Riemannian geometries over the field of two elements as the extreme case of a finite-field adaptation of noncommutative-geometric methods for physics. We classify all parallelisable geometries for coordinate algebras up to vector space dimension , finding a rich moduli of examples for n = 3 and top form degree 2, including many which are not flat. Their coordinate algebras are commutative but their differentials are not. We also study the quantum Laplacian on our models and characterise when it has a massive eigenvector.
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