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On family rigidity theorems II

Kefeng Liu Xiaonan Ma

Differential Geometry mathscidoc:1912.43113

arXiv preprint math/9911035, 1999.11
In LM, we proved a family version of the famous Witten rigidity theorems and several family vanishing theorems for elliptic genera. In this paper, we gerenalize our theorems LM in two directions. First we establish a family rigidity theorem for the Dirac operator on loop space twisted by general positive energy loop group representations. Second we prove a family rigidity theorem for spin^ c-manifolds. Several vanishing theorems on both cases are also obtained.
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@inproceedings{kefeng1999on,
  title={On family rigidity theorems II},
  author={Kefeng Liu, and Xiaonan Ma},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111624783748673},
  booktitle={arXiv preprint math/9911035},
  year={1999},
}
Kefeng Liu, and Xiaonan Ma. On family rigidity theorems II. 1999. In arXiv preprint math/9911035. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111624783748673.
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