 Euler class of a complex line bundle (source code)

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= Euler class of a complex line bundle

The complex orientation turns a complex line bundle $L$ into an oriented real rank-two bundle, and
$$
e(L_\mathbb R)=c_1(L).
$$
Moreover $e(L^*)=-e(L)$ and $e(L_1\otimes_\mathbb C L_2)=e(L_1)+e(L_2)$.

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