hairy ball theorem
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Hairy ball theorem — The hairy ball theorem of algebraic topology states that there is no nonvanishing continuous tangent vector field on the sphere. If f is a continuous function that assigns a vector in R3 to every point p on a sphere such that f ( p ) is always… … Wikipedia
Poincaré–Hopf theorem — In mathematics, the Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem) is an important theorem in differential topology. It is named after Henri Poincaré and Heinz Hopf.The… … Wikipedia
Topology — (Greek topos , place, and logos , study ) is the branch of mathematics that studies the properties of a space that are preserved under continuous deformations. Topology grew out of geometry, but unlike geometry, topology is not concerned with… … Wikipedia
Chern class — In mathematics, in particular in algebraic topology and differential geometry, the Chern classes are characteristic classes associated to complex vector bundles. Chern classes were introduced by Shiing Shen Chern (1946). Contents 1 Basic… … Wikipedia
Teorema de la bola peluda — Si un campo vectorial sobre una esfera se simboliza por pelos de longitud constante, el teorema de la bola peluda estipula que la esfera contiene al menos un rizo. La figura contiene dos, uno en cada polo. En matemática, y más precisamente en… … Wikipedia Español
mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… … Universalium
Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… … Wikipedia
Vector fields on spheres — In mathematics, the discussion of vector fields on spheres was a classical problem of differential topology, beginning with the hairy ball theorem, and early work on the classification of division algebras.Specifically, the question is how many… … Wikipedia
Lemme de Milnor — Théorème de la boule chevelue Si un champ de vecteurs sur une sphère est symbolisé par des cheveux de longueur constante, le théorème de la boule chevelue stipule que la sphère contient au moins un épi. La figure en contient deux, un sur chaque… … Wikipédia en Français
Theoreme de la boule chevelue — Théorème de la boule chevelue Si un champ de vecteurs sur une sphère est symbolisé par des cheveux de longueur constante, le théorème de la boule chevelue stipule que la sphère contient au moins un épi. La figure en contient deux, un sur chaque… … Wikipédia en Français
