trivial fibration

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• Fibration — In mathematics, especially algebraic topology, a fibration is a continuous mapping:p:E o B,satisfying the homotopy lifting property with respect to any space. Fiber bundles (over paracompact bases) constitute important examples. In homotopy… …   Wikipedia

• Hopf fibration — In the mathematical field of topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a 3 sphere (a hypersphere in four dimensional space) in terms of circles and an ordinary sphere. Discovered by Heinz Hopf in 1931, it… …   Wikipedia

• Model category — In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ( arrows ) called weak equivalences , fibrations and cofibrations . These abstract from a conventional homotopy category, of… …   Wikipedia

• Symplectic manifold — In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2 form, ω, called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology.… …   Wikipedia

• Blowing up — This article is about the mathematical concept of blowing up. For information about the physical/chemical process, see Explosion. For other uses of Blow up , see Blow up (disambiguation). Blowup of the affine plane. In mathematics, blowing up or… …   Wikipedia

• Ehresmann's theorem — In mathematics, Ehresmann s fibration theorem states that a smooth mapping : f : M → N where M and N are smooth manifolds, such that# f is a submersion, and # f is a proper map,is a locally trivial fibration. This is a foundational result in… …   Wikipedia

• Grothendieck–Hirzebruch–Riemann–Roch theorem — In mathematics, specifically in algebraic geometry, the Grothendieck–Riemann–Roch theorem is a far reaching result on coherent cohomology. It is a generalisation of the Hirzebruch–Riemann–Roch theorem, about complex manifolds, which is itself a… …   Wikipedia

• Normal invariant — In mathematics, a normal map is a concept in geometric topology due to William Browder which is of fundamental importance in surgery theory. Given a Poincaré complex X, a normal map on X endows the space, roughly speaking, with some of the… …   Wikipedia

• TOPOLOGIE - Topologie algébrique — Inventée au début du XXe siècle pour résoudre des problèmes géométriques, la topologie algébrique connut un grand développement grâce à l’introduction de constructions algébriques de plus en plus abstraites. Pour clarifier l’exposé, on a… …   Encyclopédie Universelle

• Fibré —  Pour l’article homonyme, voir Fibre.   Ne pas confondre avec une fibration ni avec un espace filtré. En mathématiques, un espace fibré est la donnée d un espace topologique appelé espace total muni d une projection continue sur un …   Wikipédia en Français

• Fibré de Seifert — En topologie, un fibré de Seifert est une variété de dimension 3 munie d une « bonne » partition en cercles. Plus précisément, c est un fibré en cercles sur un orbifold de dimension 2. Ces variétés ont été introduites par Herbert… …   Wikipédia en Français