Abstract
In this paper, we define a relative equivariant coarse index for proper actions and a relative L2-index. We derive a relative equivariant coarse index theorem connecting the relative equivariant coarse index with the localized equivariant coarse index. Furthermore, we present a calculation formula on the relative L2-index and provide a relative L2-index theorem. Our work is an expansion of the relative index theory which reflects the difference between two manifolds.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant Nos. 11771092, 11831006, 11771143 and 11801178). The authors thank Yi-Jun Yao, Xiang Tang, Shengzhi Xu and Hang Wang for many stimulating discussions.
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Chen, X., Liu, Y. & Zhou, D. Relative equivariant coarse index and relative L2-index. Sci. China Math. 66, 1449–1472 (2023). https://doi.org/10.1007/s11425-021-1990-4
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DOI: https://doi.org/10.1007/s11425-021-1990-4