A vanishing theorem for the Mathai-Zhang index
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Abstract:
We establish a vanishing theorem for spin manifolds admitting proper cocompact Lie group actions. To be more precise, when the connected component of the identity element in the action group is non-unimodular, we prove that the Mathai-Zhang index [Adv. Math. 225 (2010), pp. 1224–1247] vanishes.References
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Additional Information
- Xin Zhang
- Affiliation: Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070, People’s Republic of China
- Email: zhangxmath@whut.edu.cn
- Received by editor(s): February 11, 2022
- Received by editor(s) in revised form: February 12, 2022
- Published electronically: June 16, 2022
- Additional Notes: The work was supported by the National Natural Science Foundation of China (Grant No. 12001409)
- Communicated by: Jiaping Wang
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 4959-4964
- MSC (2020): Primary 53C27, 58J20
- DOI: https://doi.org/10.1090/proc/16038
- MathSciNet review: 4489326