Euler class in a generalized cohomology theory
= Euler class in a generalized cohomology theory
{title2=$e_h(\xi)=z^*u_\xi$}
For an $h$-oriented real bundle $\xi$ of rank $r$, pull its <Thom class> back along the <zero section> to obtain its Euler class in $h^r(X)$. It depends on the orientation and the actual bundle, not merely its stable isomorphism class. In <complex cobordism> the orientation may be supplied by a <stable complex structure on a real vector bundle>.