Eta-invariants, Torsion forms and Flat vector bundles

2004/05/31 by Xiaonan Ma, Ma, Xiaonan, weiping Zhang +1
Mathematics · #58J #Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.DG #math.KT #msc:58J

paper · pdf · doi:10.48550/arxiv.math/0405599

42 pages

arxiv created 2004/05/31 · arxiv updated 2009/12/01

Abstract

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 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.

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• Adiabatic limit, Bismut-Freed connection, and the real analytic torsion form
• η-invariant and flat vector bundles II
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