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We compute the alpha invariant of any smooth complex projective spin completeintersection of complex dimension $1 \; ({\rm mod} \; 4)$. We prove that thealpha invariant depends only on the total degree and Pontryagin classes. Ourfindings are consistent with a long-standing conjecture, often called theSullivan Conjecture, which states that two complete intersections with the samedimensions, total degrees, Pontryagin and Euler classes are diffeomorphic.

The alpha invariant of complete intersections