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A mod 2 index theorem for the twisted Signature operator

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Abstract

A mod 2 index theorem for the twisted Signature operator on 4 q + 1 dimensional manifolds is established. This result generalizes a result of Farber and Turaev, which was proved for the case of orthogonal flat bundles, to arbitrary real vector bundles. It also provides an analytic interpretation of the sign of the Poincare-Reidemeister scalar product defined by Farber and Turaev.

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Authors and Affiliations

  1. Nankai Institute of Mathematics, Nankai University, 300071, Tianjin, China

    Weiping Zhang

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  1. Weiping Zhang
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Additional information

Project partially supported by the National Natural Science Foundation of China (Grant No. 19525102), the Fok Ying-Tung Foundation and the Qiu Shi Foundation.

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Zhang, W. A mod 2 index theorem for the twisted Signature operator. Sci. China Ser. A-Math. 42, 1279–1285 (1999). https://doi.org/10.1007/BF02876028

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  • DOI: https://doi.org/10.1007/BF02876028

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