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

Details Index theory with bounded geometry, the uniformly finite A-hat class, and infinite connected sums Index theory with bounded geometry, the uniformly finite A-hat class, and infinite connected sums

2004-05-14

arxiv.org/abs/math/0405271v1

JDG 59, 2001

Mathematics

Differential Geometry

Scientific paper

We analyze the obstruction to metrics of positive scalar curvature within a given bounded distortion class of metrics. This obstruction lives in a non-Hausdorff cohomology group Poincare dual to the uniformly finite homology studied by Block and Weinberger. One of the applications is a converse to their theorem on infinite connected sums, giving a complete picture of when such manifolds have metrics of positive scalar curvature.

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