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Rigidity and vanishing theorems on $ {\mathbb{Z}}/k$ Spin$ ^c$ manifolds


Authors: Bo Liu and Jianqing Yu
Journal: Trans. Amer. Math. Soc. 367 (2015), 1381-1420
MSC (2010): Primary 58J26
DOI: https://doi.org/10.1090/S0002-9947-2014-06273-9
Published electronically: July 18, 2014
MathSciNet review: 3280048
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Abstract: In this paper, we first establish an $ S^1$-equivariant index theorem for Spin$ ^c$ Dirac operators on $ \mathbb{Z}/k$ manifolds, and then combining this equivariant index theorem with the methods developed by Liu-Ma-Zhang and Taubes, we extend Witten's rigidity theorem to the case of $ \mathbb{Z}/k$ Spin$ ^c$ manifolds. Among others, our results resolve a conjecture of Devoto.


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Additional Information

Bo Liu
Affiliation: Chern Institute of Mathematics & LPMC, Nankai University, Tianjin 300071, People’s Republic of China
Address at time of publication: Mathematisches Institut, Universität zu Köln, Wyertal 86-90, D50931 Köln, Germany
Email: boliumath@mail.nankai.edu.cn, boliumath@gmail.com

Jianqing Yu
Affiliation: Chern Institute of Mathematics & LPMC, Nankai University, Tianjin 300071, People’s Republic of China
Address at time of publication: University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui 230026, People’s Republic of China
Email: jianqingyu@gmail.com

DOI: https://doi.org/10.1090/S0002-9947-2014-06273-9
Received by editor(s): June 21, 2012
Received by editor(s) in revised form: June 19, 2013
Published electronically: July 18, 2014
Additional Notes: The authors wish to thank Professors Daniel S. Freed, Xiaonan Ma and Weiping Zhang for their helpful discussions. They would also like to thank the referees for valuable suggestions
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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