K-Homology, Assembly and Rigidity Theorems for Relative Eta Invariants
نویسندگان
چکیده
Nigel Higson and John Roe Abstract: We connect the assembly map in C∗-algebra K-theory to rigidity properties for relative eta invariants that have been investigated by Mathai, Keswani, Weinberger and others. We give a new and conceptual proof of Keswani’s theorem that whenever the C∗-algebra assembly map is an isomorphism, the relative eta invariants associated to the signature operator are homotopy invariants, whereas the relative eta invariants associated to the Dirac operator on a manifold with positive scalar curvature vanish.
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