Section
From HandWiki
This category corresponds roughly to MSC {{{id}}} {{{title}}}; see {{{id}}} at MathSciNet and {{{id}}} at zbMATH.
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
| [1] | E.H. Spanier, "Algebraic topology", McGraw-Hill (1966) pp. 77 MR0210112 MR1325242 Template:ZBL |
 |  |
