Euler class

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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.


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.


[a1] E.H. Spanier, "Algebraic topology" , McGraw-Hill (1966) pp. 156
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Euler class. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.F. Kharshiladze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article