Euler class
Characteristic class of oriented, real vector bundles / From Wikipedia, the free encyclopedia
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In mathematics, specifically in algebraic topology, the Euler class is a characteristic class of oriented, real vector bundles. Like other characteristic classes, it measures how "twisted" the vector bundle is. In the case of the tangent bundle of a smooth manifold, it generalizes the classical notion of Euler characteristic. It is named after Leonhard Euler because of this.
Throughout this article is an oriented, real vector bundle of rank
over a base space
.