= A nowhere-zero section annihilates generalized Euler classes
{title2=$s(x)\ne0\text{ for all }x\quad\Longrightarrow\quad e_h(\xi)=0$}
Normalize the section to the <sphere bundle>. Scaling it from zero to unit length gives a <homotopy> within the <disk bundle> from the <zero section> to this sphere-valued section. The image of the relative <Thom class> in absolute cohomology restricts to zero on the <sphere bundle>. <Homotopy> invariance therefore makes its zero-section pullback vanish.
// Target: geometry-and-topology.bigb
Back to article page
