Open Access
May 2011 Generalized Witten Genus and Vanishing Theorems
Qingtao Chen, Fei Han, Weiping Zhang
J. Differential Geom. 88(1): 1-39 (May 2011). DOI: 10.4310/jdg/1317758867


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 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 generalizedWitten 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. "Generalized Witten Genus and Vanishing Theorems." J. Differential Geom. 88 (1) 1 - 39, May 2011.


Published: May 2011
First available in Project Euclid: 4 October 2011

zbMATH: 1252.58011
MathSciNet: MR2819754
Digital Object Identifier: 10.4310/jdg/1317758867

Rights: Copyright © 2011 Lehigh University

Vol.88 • No. 1 • May 2011
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