Eta-invariants, torsion forms and flat vector bundles

摘要

We present a new proof, as well as a C/Q extension (and also certain C/Z extension), of the Riemann-Roch-Grothendieck theorem of Bismut-Lott for flat vector bundles. The main techniques used are the computations of the adiabatic limits of eta-invariants associated to the so-called sub-signature operators. We further show that the Bismut-Lott analytic torsion form can be derived naturally from transgressions of eta-forms appearing in the adiabatic limit computations.