Section
From Encyclopedia of Mathematics - Reading time: 1 min
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 $p\circ s={\rm id}_Y$.
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.
References[edit]
| [Sp] | E.H. Spanier, "Algebraic topology", McGraw-Hill (1966) pp. 77 MR0210112 MR1325242 Zbl 0145.43303 |
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