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Eta-invariants, torsion forms and flat vector bundles

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Abstract

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 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 transgressions of η-forms appearing in the adiabatic limit computations.

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Authors and Affiliations

  1. Centre de Mathématiques Laurent Schwartz, UMR 7640 du CNRS, École Polytechnique, 91128, Palaiseau Cedex, France

    Xiaonan Ma

  2. Chern Institute of Mathematics & LPMC, Nankai University, Tianjin, 300071, People’s Republic of China

    Weiping Zhang

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  1. Xiaonan Ma
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  2. Weiping Zhang
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Correspondence to Weiping Zhang.

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Ma, X., Zhang, W. Eta-invariants, torsion forms and flat vector bundles. Math. Ann. 340, 569–624 (2008). https://doi.org/10.1007/s00208-007-0160-9

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  • DOI: https://doi.org/10.1007/s00208-007-0160-9

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