Euler number of a vector bundle
= Euler number of a vector bundle
{title2=$\langle e(E),[B]\rangle$}
When an oriented rank-$d$ vector bundle $E$ has a closed oriented $d$-dimensional base $B$, its Euler number is the integer obtained by evaluating the <Euler class of a vector bundle> on the <fundamental class> of $B$. A nonzero Euler number obstructs a nowhere-zero section and therefore obstructs a framing.