Generalized Witten Genus and Vanishing Theorems

Qingtao Chen; Fei Han; Weiping Zhang

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arXiv · 1003.2325

Generalized Witten Genus and Vanishing Theorems

Qingtao Chen·Fei Han·Weiping Zhang

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Abstract

We construct a generalized Witten genus for spin$^c$ manifolds, which takes values in level 1 modular forms with integral Fourier expansion on a class of spin$^c$ manifolds called string$^c$ manifolds. We also construct a mod 2 analogue of the Witten genus for $8k+2$ dimensional spin manifolds. The Landweber-Stong type vanishing theorems are proven for the generalized Witten genus and the mod 2 Witten genus on string$^c$ and string (generalized) complete intersections in (product of) complex projective spaces respectively.

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Qingtao Chen, Fei Han, Weiping Zhang. 2010-03-11. Generalized Witten Genus and Vanishing Theorems. https://arxiv.org/abs/1003.2325

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