Eta-invariants, Torsion forms and Flat vector bundles

الأصل · EN

We present a new proof, as well as a C/Q 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 η-invariants associated to the so-called sub-signature operators. We further show that the Bismut-Lott analytic torsion form can be derived naturally from the transgression of the η-forms appearing in the adiabatic limit computations.