Difference between revisions of "Section"
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[[Principal fibre bundle|principal fibre bundle]] the existence of a section implies its triviality. A | [[Principal fibre bundle|principal fibre bundle]] the existence of a section implies its triviality. A | ||
[[Vector bundle|vector bundle]] always possesses the so-called zero section. | [[Vector bundle|vector bundle]] always possesses the so-called zero section. | ||
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Latest revision as of 22:27, 24 November 2013
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
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