Diffeomorphisms and Noncommutative Analytic Torsion
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Abstract. We prove an index theorem concerning the pushforward of flat ${\mathfrak B}$-vector bundles, where ${\mathfrak B}$ is an appropriate algebra. We construct an associated analytic torsion form ${\mathcal T}$. If $Z$ is a smooth closed aspherical manifold, we show that ${\mathcal T}$ gives invariants of $\pi_*(\mathrm{Diff}(Z))$.
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