Asymptotic Fredholm Modules, Vector Bundles with Small Variation and a Nonvanishing Theorem for K-Theoretic Indices*

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Abstract

We introduce the concept of asymptotic Fredholm module to prove a nonvanishing theorem for K theoretic indices of elliptic operators. The nonvanishing theorem is applied to study positive scalar curvature and spectrum of the Laplacian on noncompact manifolds.

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