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Real embeddings, eta invariant and Chern-Simons current

We present an alternate proof of the Bismut-Zhang localization formula for $η$-invariants without using the analytic techniques developed by Bismut-Lebeau. A Riemann-Roch property for Chern-Simons currents, which is of independent interest, is established in due course.

preprint2007arXivOpen access

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