| Abstract: |
We connect the assembly map in C*-algebra K-theory to rigidity prop-
erties 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 iso-
morphism, 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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