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Asymptotics of the Eta Invariant

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Abstract

We prove an asymptotic bound on the eta invariant of a family of coupled Dirac operators on an odd dimensional manifold. In the case when the manifold is the unit circle bundle of a positive line bundle over a complex manifold, we obtain precise formulas for the eta invariant.

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Authors and Affiliations

  1. Département de Mathématique, Université Paris-Sud, 91405, Orsay, France

    Nikhil Savale

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  1. Nikhil Savale
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Correspondence to Nikhil Savale.

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Communicated by S. Zelditch

The research leading to the results contained in this paper has received funding from the European Research Council (E.R.C.) under the European Union’s Seventh Framework Program (FP7/2007-2013)/ERC grant agreement No. 291060.

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Savale, N. Asymptotics of the Eta Invariant. Commun. Math. Phys. 332, 847–884 (2014). https://doi.org/10.1007/s00220-014-2114-x

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  • DOI: https://doi.org/10.1007/s00220-014-2114-x

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