The equivariant family index theorem in odd dimensions |
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| Authors: | Kai Hua Bao Jian Wang Yong Wang |
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| Institution: | 1. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, P. R. China;
2. School of Science, Tianjin University of Technology and Education, Tianjin 300222, P. R. China;
3. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, P. R. China |
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| 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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| Keywords: | Odd equivariant family index formula Chern-Connes character Atiyah-Hirzebruch vanishing theorem |
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