Generalized Witten Genus and Vanishing Theorems

Details Generalized Witten Genus and Vanishing Theorems Generalized Witten Genus and Vanishing Theorems

2010-03-11

arxiv.org/abs/1003.2325v1

JDG, 88 (2011) 1-39

Mathematics

Differential Geometry

28 pages

Scientific paper

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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