Rigidity and vanishing theorems in K-theory

Kefeng Liu Xiaonan Ma Weiping Zhang

K-Theory and Homology mathscidoc:1912.43073

Communications in Analysis and Geometry, 11, (1), 121-180, 2003.1
In [W], Witten considered the indices of elliptic operators on the free loop space CM of a spin manifold M. In particular the index of the formal signature operator on the loop space is exactly the elliptic genus of Landweber-Stong-Ochanine [LS],[O]. Motivated by physics, Witten made the conjectures about the rigidity of these elliptic operators which say that their 51-equivariant indices on M are independent of g G Sl. See [L] for the early history of the subject.
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  title={Rigidity and vanishing theorems in K-theory},
  author={Kefeng Liu, Xiaonan Ma, and Weiping Zhang},
  booktitle={Communications in Analysis and Geometry},
Kefeng Liu, Xiaonan Ma, and Weiping Zhang. Rigidity and vanishing theorems in K-theory. 2003. Vol. 11. In Communications in Analysis and Geometry. pp.121-180. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111406857825633.
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