Abstract
In this paper, we prove a local odd dimensional equivariant family index theorem which generalizes Freed’s odd dimensional index formula. Then we extend this theorem to the noncommutative geometry framework. As a corollary, we get the odd family Lichnerowicz vanishing theorem and the odd family Atiyah-Hirzebruch vanishing theorem.
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Supported by National Natural Science Foundation of China (Grant No. 11271062) and Program for New Century Excellent Talents in University (Grant No. 13-0721)
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Bao, K.H., Wang, J. & Wang, Y. The equivariant family index theorem in odd dimensions. Acta. Math. Sin.-English Ser. 31, 1149–1162 (2015). https://doi.org/10.1007/s10114-015-3637-6
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DOI: https://doi.org/10.1007/s10114-015-3637-6