Infinite connected sums, K-area and positive scalar curvature

Details Infinite connected sums, K-area and positive scalar curvature Infinite connected sums, K-area and positive scalar curvature

2004-08-17

arxiv.org/abs/math/0408228v2

Mathematics

Differential Geometry

12 pages, no figures

Scientific paper

Recently, Whyte used the index theory of Dirac operators and the Block-Weiberger uniformly finite homology to show that certain infinite connected sums do not carry a metric with nonnegative scalar curvature in their bounded geometry class. His proof uses a generalization of the $\hat{A}$-class to obstruct such metrics. In this note we prove a variant of Whyte's result where infinite $K$-area in the sense of Gromov is used to obstruct metrics with positive scalar curvature.

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