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Transactions of the American Mathematical Society

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String$ ^c$ structures and modular invariants


Authors: Ruizhi Huang, Fei Han and Haibao Duan
Journal: Trans. Amer. Math. Soc. 374 (2021), 3491-3533
MSC (2020): Primary 53C27, 55R35, 57S15; Secondary 57R20, 22E67, 55R40
DOI: https://doi.org/10.1090/tran/8311
Published electronically: January 27, 2021
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Abstract: In this paper, we study some algebraic topology aspects of String$ ^c$ structures, more precisely, from the perspective of Whitehead tower and the perspective of the loop group of $ Spin^c(n)$. We also extend the generalized Witten genera constructed for the first time by Chen et al. [J. Differential Geom. 88 (2011), pp. 1-40] to correspond to String$ ^c$ structures of various levels and give vanishing results for them.


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Additional Information

Ruizhi Huang
Affiliation: Institute of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
Email: huangrz@amss.ac.cn

Fei Han
Affiliation: Department of Mathematics, National University of Singapore, Singapore 119076
Email: mathanf@nus.edu.sg

Haibao Duan
Affiliation: Institute of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
Email: dhb@math.ac.cn

DOI: https://doi.org/10.1090/tran/8311
Received by editor(s): November 4, 2019
Received by editor(s) in revised form: September 2, 2020
Published electronically: January 27, 2021
Additional Notes: The first author was supported by Postdoctoral International Exchange Program for Incoming Postdoctoral Students under Chinese Postdoctoral Council and Chinese Postdoctoral Science Foundation. He was also supported in part by Chinese Postdoctoral Science Foundation (Grant nos. 2018M631605 and 2019T120145), and National Natural Science Foundation of China (Grant no. 11801544).
The second author was partially supported by the grant AcRF R-146-000-263-114 from National University of Singapore.
The third author was partially supported by National Natural Science Foundation of China (Grant nos. 11131008 and 11661131004).
Article copyright: © Copyright 2021 American Mathematical Society