= Stable complex structure on a real vector bundle
For an even-rank real <vector bundle> $\xi$, a stable complex structure is a complex structure on $\xi\oplus\mathbb R^{2s}$, considered up to adding trivial complex bundles and homotopy. This gives a stable complex class but does not necessarily make $\xi$ itself a complex vector bundle. Stable Chern classes therefore need not recover the unstable <Euler class>: $TS^4\oplus\mathbb R^2$ can be made trivial complex, while $e(TS^4)$ evaluates to $2$.
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