= Product of linear projective subspaces in complex cobordism
{title2=$[\mathbb{CP}^{k},\nu_k]\,[\mathbb{CP}^{m},\nu_m]=[\mathbb{CP}^{k+m-n},\nu_{k+m-n}]$}
The displayed product applies when $k+m\geq n$. Move one projective subspace by a unitary <isotopy> into transverse position. The intersection is a linear projective subspace of dimension $k+m-n$, with normal complex bundle the sum of the restricted input <normal bundles>. If $k+m<n$, representatives can be made disjoint and the product is zero.
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