 Euler class of a complex line bundle

ID: 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_{R}) = c_{1} (L) .

Moreover

e (L^{*}) = - e (L)

and

e (L_{1} \otimes_{C} L_{2}) = e (L_{1}) + e (L_{2})

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