The alpha invariant of complete intersections

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