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Regularity of the eta function on manifolds with cusps

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Abstract

On a spin manifold with conformal cusps, we prove under an invertibility condition at infinity that the eta function of the twisted Dirac operator has at most simple poles and is regular at the origin. For hyperbolic manifolds of finite volume, the eta function of the Dirac operator twisted by any homogeneous vector bundle is shown to be entire.

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Authors and Affiliations

  1. Department of Mathematics, Binghamton University, Binghamton, NY, 13902, USA

    Paul Loya

  2. Institutul de Matematică al Academiei Române, P.O. Box 1-764, 014700, Bucharest, Romania

    Sergiu Moroianu

  3. Scoala Normală Superioară Bucharest, calea Grivitei 21, Bucharest, Romania

    Sergiu Moroianu

  4. School of Mathematics, Korea Institute for Advanced Study, Hoegiro 87, Dongdaemun-gu, Seoul, 130-722, Korea

    Jinsung Park

Authors
  1. Paul Loya
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  2. Sergiu Moroianu
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  3. Jinsung Park
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Corresponding author

Correspondence to Jinsung Park.

Additional information

SM was partially supported by grant PN-II-ID-PCE 1188 265/2009. PL was partially supported by NSF grant 0757795.

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Loya, P., Moroianu, S. & Park, J. Regularity of the eta function on manifolds with cusps. Math. Z. 269, 955–975 (2011). https://doi.org/10.1007/s00209-010-0769-3

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  • DOI: https://doi.org/10.1007/s00209-010-0769-3

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