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

Yu, Guoliang

Department of Mathematics, University of Colorado, Boulder, CO 80309, U.S.A. e-mail: [email protected]

K-Theory 13(4):p 331-346, April 1998.

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.

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

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