Namespaces
Variants
Actions

Difference between revisions of "Section"

From Encyclopedia of Mathematics
Jump to: navigation, search
m (tex,MR,ZBL,MSC, refs)
m (empty comment removed)
 
Line 15: Line 15:
 
[[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.
 
 
 
====Comments====
 
  
  

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
This article was adapted from an original article by A.F. Kharshiladze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article