= Chern number
{c}
{title2=$\langle c_{i_1}\cdots c_{i_s},[M]\rangle$}
On a compact oriented $2r$-manifold without boundary, an integral product of <Chern classes> of total complex degree $r$ pairs with the <fundamental class> to give a <Chern number>. A <unitary connection> supplies <Chern-Weil theory> representatives, but the integer is independent of that connection. The <Second Chern number> on a four-manifold is one important example; the integral of the <First Chern class> over a closed surface is another.
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