Eta-invariants, Torsion forms and Flat vector bundles

Details Eta-invariants, Torsion forms and Flat vector bundles Eta-invariants, Torsion forms and Flat vector bundles

2004-05-31

arxiv.org/abs/math/0405599v1

Mathematics

Differential Geometry

42 pages

Scientific paper

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

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