First Chern class
= First Chern class
{c}
{title2=$c_1(E)$}
{wiki=Chern_class}
The first Chern class classifies complex line bundles topologically. For a Hermitian holomorphic line bundle with Chern curvature $F_\nabla$, Chern-Weil theory gives $c_1(E)=[iF_\nabla/(2\pi)]$.