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Block and Weinberger show that an arithmetic manifold can be endowed with a positive scalar curvature metric if and only if its Q-rank exceeds2. We show in this article that these metrics are never in the same coarse class as the natural metric inherited from the base Lie group. Furthering the coarse C -algebraic methods of Roe, we find a nonzero Dirac obstruction in the Ktheory of a particular operator algebra which encodes information about the quasi-isometry type of the manifold as well as its local geometry.

Coarse Obstructions to Positive Scalar Curvature in Noncompact Arithmetic Manifolds