## Journal of Differential Geometry

### Generalized Witten Genus and Vanishing Theorems

#### 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 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.

#### Article information

Source
J. Differential Geom., Volume 88, Number 1 (2011), 1-39.

Dates
First available in Project Euclid: 4 October 2011

https://projecteuclid.org/euclid.jdg/1317758867

Digital Object Identifier
doi:10.4310/jdg/1317758867

Mathematical Reviews number (MathSciNet)
MR2819754

Zentralblatt MATH identifier
1252.58011

#### Citation

Chen, Qingtao; Han, Fei; Zhang, Weiping. Generalized Witten Genus and Vanishing Theorems. J. Differential Geom. 88 (2011), no. 1, 1--39. doi:10.4310/jdg/1317758867. https://projecteuclid.org/euclid.jdg/1317758867