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.
| Original language | English |
|---|---|
| Pages (from-to) | 1-39 |
| Number of pages | 39 |
| Journal | Journal of Differential Geometry |
| Volume | 88 |
| Issue number | 1 |
| Publication status | Published - May 2011 |