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Adiabatic limit, Bismut-Freed connection, and the real analytic torsion form. (English) Zbl 1215.58017
The authors consider a fibered manifold \(\pi: M\to B\) with fiber \(Z\) and a metric on \(M\) of the form \(g_\varepsilon = \varepsilon^{-2} \pi^\ast g_B+g_Z\) where \(\varepsilon \to 0\) and \(g_B\), \(g_Z\) are fixed Riemannian metrics on the base and the fiber, correspondingly. The authors define an analytic torsion invariant via zeta function regularization. They compute the adiabatic limit of the Bismut-Freed connection associated to a family of deformed sub-signature operators introduced by Ma and Zhang and identify in the answer the Bismut-Lott analytic torsion form.

MSC:
58J52 Determinants and determinant bundles, analytic torsion
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