# Euler class

From Encyclopedia of Mathematics

The first obstruction in the construction of sections of a fibration the fibre of which is a sphere, associated with a vector bundle. See Characteristic class.

#### Comments

Multiplication by the Euler class (sometimes called the orientation class) is one of the homeomorphisms in the Gysin sequence of an oriented sphere bundle [a1]. The Euler characteristic of a compact, oriented $n$-dimensional manifold may be calculated from the Euler class of the tangent bundle [a1], p. 348.

#### References

[a1] | E.H. Spanier, "Algebraic topology" , McGraw-Hill (1966) pp. 156 |

**How to Cite This Entry:**

Euler class.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Euler_class&oldid=31830

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