Section

2020 Mathematics Subject Classification: Primary: 14-XX [MSN][ZBL]

A section or section surface of a surjective (continuous) map or of a fibre space $p:X\to Y$ is a (continuous) mapping $s:Y\to X$ such that $p\circ s={\mathrm{i}\mathrm{d}}_Y$.

If $(X,p,Y)$ is a Serre fibration, then

$${\pi }_n(X)={\pi }_n(p^{-1}(pt))\oplus {\pi }_n(Y).$$ For a principal fibre bundle the existence of a section implies its triviality. A vector bundle always possesses the so-called zero section.

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