We prove a vanishing theorem in uniformly finite homology for the Â genus of a complete spin manifold of bounded geometry and non-negative scalar curvature. This theorem is then applied to obstruct the existence of such metrics for some infinite connected sums, giving a converse to a theorem of Block and Weinberger.
"Index Theory with Bounded Geometry, the Uniformly Finite Â Class, and Infinite Connected Sums." J. Differential Geom. 59 (1) 1 - 14, September, 2001. https://doi.org/10.4310/jdg/1090349278