Self-intersection formula in complex cobordism
= Self-intersection formula in complex cobordism
{title2=$i^*i_!(a)=a\,e_{MU}(\nu_i)$}
Restricting the tubular-neighborhood collapse of an embedding back to its source is the normal bundle's zero section. The <Thom isomorphism in complex cobordism> therefore makes pullback after the Gysin map multiplication by the <Euler class in a generalized cohomology theory>. For an actual complex normal bundle this is its top <Chern class in complex cobordism>.