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A mod 2 index theorem for pin− manifolds

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Abstract

We establish a mod 2 index theorem for real vector bundles over 8k + 2 dimensional compact pin− manifolds. The analytic index is the reduced η invariant of (twisted) Dirac operators and the topological index is defined through KO-theory. Our main result extends the mod 2 index theorem of Atiyah and Singer (1971) to non-orientable manifolds.

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Acknowledgements

This work was supported by National Science Foundation of USA (Grant No. DMS 9022140) through a Mathematical Sciences Research Institute (MSRI) postdoctoral fellowship.

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  1. Chern Institute of Mathematics & LPMC, Nankai University, Tianjin, 300071, China

    WeiPing Zhang

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  1. WeiPing Zhang
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Zhang, W. A mod 2 index theorem for pin− manifolds. Sci. China Math. 60, 1615–1632 (2017). https://doi.org/10.1007/s11425-016-9040-7

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  • DOI: https://doi.org/10.1007/s11425-016-9040-7

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