= Thom class in a generalized cohomology theory
{c}
{title2=$u_h(\xi)\in h^r(D(\xi),S(\xi))$}
For an $h$-oriented rank-$r$ real <vector bundle>, its <Thom class> restricts on each fiber to the suspension of the coefficient unit under the oriented identification $h^r(D^r,S^{r-1})\cong h^0(\mathrm{pt})$. <Cup product> with this class gives the Thom isomorphism. The associated <Euler class in a generalized cohomology theory> is the pullback along the <zero section> after forgetting relative supports.
// Target: geometry-and-topology.bigb
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