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There are a well-known facts about Dixmier trace and Wodzicki residue. Let $P$ be an elliptic pseudodifferential operator of degree $−n$ on a compact Riemannian manifold $(M,g)$, than its Dixmier ...

What I want to ask is the multiplicativity of the analytic index of a family of Dirac operators. In the single operator case the analytic index of elliptic operator is multiplicative. This is proved ...