String^{𝑐} structures and modular invariants

Huang, Ruizhi; Han, Fei; Duan, Haibao

doi:10.1090/tran/8311

String$^c$ structures and modular invariants
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by Ruizhi Huang, Fei Han and Haibao Duan PDF

Trans. Amer. Math. Soc. 374 (2021), 3491-3533 Request permission

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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