Namespaces
Variants
Actions

Section

From Encyclopedia of Mathematics
Jump to: navigation, search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

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

[Sp] E.H. Spanier, "Algebraic topology", McGraw-Hill (1966) pp. 77 MR0210112 MR1325242 Zbl 0145.43303
How to Cite This Entry:
Section. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Section&oldid=30774
This article was adapted from an original article by A.F. Kharshiladze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article