Abstract
We construct a mod 2 analogue of the Witten genus for 8 k + 2 dimensional spin manifolds, as well as modular characteristic numbers for a class of spin c manifolds which we call string c manifolds. When these spin c manifolds are actually spin, one recovers the original Witten genus on string manifolds. These genera vanish on string and string c complete intersections respectively in complex projective spaces.
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