Generalized Witten Genus and Vanishing Theorems
Abstract
We construct a generalized Witten genus for spinc manifolds, which takes values in level 1 modular forms with integral Fourier expansion on a class of spinc manifolds called stringc 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 stringc and string (generalized) complete intersections in (product of) complex projective spaces respectively.
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