= Cup-power obstruction to nonzero degree
Let $M,N$ be closed connected oriented manifolds of the same dimension, and suppose $a^r$ generates the top integral <cohomology> of $N$. If every class of degree $|a|$ on $M$ has zero rth <cup power>, every <continuous map> $f:M\to N$ has <mapping degree> zero. Indeed, $f^*(a^r)=(f^*a)^r=0$, and evaluation on the <fundamental class> gives $\deg f=0$. For $S^2\times S^4\to\mathbb{CP}^3$, the degree-two class is a multiple of the sphere class $u$, whose square vanishes.
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