Index theory with bounded geometry, the uniformly finite  class, and infinite connected sums

Abstract

We prove a vanishing theorem in uniformly finite homology for the  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. © Applied Probability Trust 2001.